CBSE Class 5 Mathematics Compilation Worksheet

Unit 2 - Addition and Subtraction

[I] Fill in the blanks

Question 1. When zero is added to any number the sum is __________.
Answer: the number itself
In simple words: Adding zero does not change the value of a number.

Exam Tip: Remember the additive identity property of zero: \(a + 0 = a\).

Question 2. The sum of 2 numbers remains __________ even if the order of the numbers is changed.
Answer: the same (or unchanged)
In simple words: Changing the order of addends does not alter the total sum.

Exam Tip: This is known as the commutative property of addition.

Question 3. 12516 + 0 = __________
Answer: 12516
In simple words: Any number plus zero equals that same number.

Exam Tip: Do not perform actual calculation for zero addition; just write the original number.

Question 4. 134 + 5029 = __________
Answer: 5163
In simple words: Add the two numbers vertically aligning their place values.

Exam Tip: Always align numbers by their rightmost digits (ones place) before adding.

Question 5. When 1 is added to a number, we get the __________ of the number.
Answer: successor
In simple words: Adding 1 gives the very next number counting forward.

Exam Tip: Successor means number + 1.

Question 6. The successor of 25428 is ___________.
Answer: 25429
In simple words: Add 1 to 25428 to get 25429.

Question 7. When 1 is subtracted from a number we get the __________ of the number.
Answer: predecessor
In simple words: Subtracting 1 gives the number that comes immediately before.

Exam Tip: Predecessor means number - 1.

Question 8. The predecessor of 394820 is ___________.
Answer: 394819
In simple words: Subtract 1 from 394820 to get 394819.

Exam Tip: Decrease the ones digit by 1 when borrowing is not required.

Question 9. When we subtract a number from the same number, the result is __________.
Answer: zero (0)
In simple words: Taking a quantity away from itself leaves nothing.

Exam Tip: \(a - a = 0\) for any number \(a\).

Question 10. 302645 - 302645 = ___________.
Answer: 0
In simple words: Any number subtracted by itself is zero.

Exam Tip: Recognize identical numbers in subtraction immediately.

[II] Do The Following

Question 1. Arrange in columns and solve: {a} 3904765 + 852746 + 42056
Answer:
3904765
+  852746
+   42056
-------------
4799567
In simple words: Line up all numbers by their place values and add column by column from right to left.

Exam Tip: Double check carry-overs when columns sum to more than 9.

Question 1. {b} 2804732 + 46829
Answer:
2804732
+   46829
-------------
2851561
In simple words: Align numbers properly to the right and add each column.

Exam Tip: Ensure shorter numbers are aligned correctly under the ones, tens, and hundreds columns of the larger number.

Question 1. {c} 8032641 - 6245027
Answer:
8032641
- 6245027
-------------
1787614
In simple words: Subtract column by column from right to left, borrowing when necessary.

Exam Tip: Practice borrowing carefully across zero digits in large numbers.

Question 1. {d} 7039846 - 2563404
Answer:
7039846
- 2563404
-------------
4476442
In simple words: Align by place value and subtract systematically.

Exam Tip: Check your subtraction by adding the result to the subtrahend to see if you get the minuend.

Question 2. Add the following: 1234567 + 7654321
Answer:
1234567
+ 7654321
-------------
8888888
In simple words: Add corresponding digits directly without any carries.

Exam Tip: Notice the symmetrical pattern of digits in this specific problem.

Question 2. Add the following: 2503627 + 6784594
Answer:
2503627
+ 6784594
-------------
9288221
In simple words: Add column by column from right to left with proper carrying.

Exam Tip: Keep your columns straight to avoid addition errors.

Question 2. Add the following: 8740952 + 2568234 + 439758
Answer:
8740952
+ 2568234
+  439758
-------------
11748944
In simple words: Line up all three numbers and calculate the total sum.

Question 2. Add the following: 3920618 + 5207984 + 4183627
Answer:
3920618
+ 5207984
+ 4183627
-------------
13312229
In simple words: Add the three large numbers column by column.

Exam Tip: Take extra care with column alignment when adding three numbers of equal length.

Question [III]. Subtract The Following: 9046832 - 7452396
Answer:
9046832
- 7452396
-------------
1594436
In simple words: Subtract each column from right to left, borrowing across place values where needed.

Exam Tip: When borrowing from zero, convert it to 9 and borrow from the next non-zero digit.

Question [III]. Subtract The Following: 8347529 - 212407
Answer:
8347529
-   212407
-------------
8135122
In simple words: Align the smaller number to the right and subtract.

Exam Tip: Align decimal or place value columns accurately, ensuring thousands are under thousands.

[IV] Choose the Correct Answer

Question 1. The predecessor of 704298 is ___________. {704297, 704299, 704298}
(a) 704297
(b) 704299
(c) 704298
Answer: (a) 704297
Predecessor = \(704298 - 1 = 704297\)
In simple words: Subtract 1 to find the number before.

Exam Tip: Predecessor is always 1 less than the given number.

Question 2. The successor of 526300 is ___________. {526299, 526300, 526301}
(a) 526299
(b) 526300
(c) 526301
Answer: (c) 526301
Successor = \(526300 + 1 = 526301\)
In simple words: Add 1 to find the next number.

Exam Tip: Successor is always 1 greater than the given number.

Question 3. 296389 + 1 = ___________. {1, 296390, 296391}
(a) 1
(b) 296390
(c) 296391
Answer: (b) 296390
\(296389 + 1 = 296390\)
In simple words: Adding 1 gives the successor.

Exam Tip: Adding 1 increments the last digit by 1.

Question 4. 854263 - 0 = ___________. {854263, 0, 8542630}
(a) 854263
(b) 0
(c) 8542630
Answer: (a) 854263
Subtracting zero leaves any number unchanged.
In simple words: Taking away nothing leaves the original amount.

Exam Tip: Zero property of subtraction: \(a - 0 = a\).

Question 5. 3628435 + 0 = ___________. {36284360, 4628436, 3628436}
(a) 36284360
(b) 4628436
(c) 3628436
Answer: (c) 3628436 (Note: The option text in worksheet had a typo for 3628435 + 0, which equals 3628435. Matching closest option representing the number itself if interpreted as +1 or exact match).

Exam Tip: Check options carefully for misprints in source materials.

Question 6. 750603 - 750603 = ___________. {750603, 0, 1}
(a) 750603
(b) 0
(c) 1
Answer: (b) 0
\(750603 - 750603 = 0\)
In simple words: Any number minus itself equals zero.

Question 1. The product of any number and 1 is ___________.
Answer: the number itself
In simple words: Multiplying by 1 does not change the number.

Exam Tip: Multiplicative identity property: \(a \times 1 = a\).

Question 2. The product of any number and 0 is ___________.
Answer: 0 (zero)
In simple words: Anything multiplied by zero becomes zero.

Exam Tip: Zero property of multiplication: \(a \times 0 = 0\).

Question 3. The product of any number and an even number is ___________.
Answer: an even number
In simple words: Multiplying by an even number always results in an even product.

Exam Tip: Even \(\times\) Any Integer = Even.

Question 4. The product of 2 odd numbers is always ___________.
Answer: an odd number
In simple words: Odd times odd is always odd.

Exam Tip: Odd \(\times\) Odd = Odd.

Question 5. The number that is multiplied is called the ___________.
Answer: multiplicand
In simple words: The multiplicand is the number being acted upon by the multiplier.

Exam Tip: Know your multiplication vocabulary: multiplicand \(\times\) multiplier = product.

Question 6. The number by which we multiply is called the ___________.
Answer: multiplier
In simple words: The multiplier tells how many times to take the multiplicand.

Question 7. The answer in multiplication is called ___________.
Answer: the product
In simple words: The result of multiplying numbers is the product.

Exam Tip: Product is the standard term for multiplication results.

Question 8. 62453 x 1 = ___________.
Answer: 62453
In simple words: Multiplying by 1 leaves the number unchanged.

Exam Tip: Apply the identity property instantly.

Question 9. 0 x 23460 = ___________.
Answer: 0
In simple words: Zero times any number is zero.

Exam Tip: Any expression multiplied by 0 collapses to 0.

Question 10. 7406 x 318 = ___________.
Answer: 2355108
\(7406 \times 300 = 2221800\)
\(7406 \times 10 = 74060\)
\(7406 \times 8 = 59248\)
Sum = \(2221800 + 74060 + 59248 = 2355108\)
In simple words: Multiply 7406 by each digit of 318 and add the partial products.

Exam Tip: Align partial products carefully by place value.

Question 11. The product of the largest three digit number and the smallest three digit number is ___________.
Answer: 99900
Largest 3-digit number = 999
Smallest 3-digit number = 100
Product = \(999 \times 100 = 99900\)
In simple words: Multiply 999 by 100 by appending two zeros.

Exam Tip: Largest 3-digit is 999; smallest 3-digit is 100.

Question 12. 400 x 70 = ___________.
Answer: 28000
\(4 \times 7 = 28\), add 3 zeros = 28000
In simple words: Multiply the non-zero digits and attach all trailing zeros.

Exam Tip: Count total zeros in both factors (2 + 1 = 3 zeros).

Question 13. 100 x 519 = ___________.
Answer: 51900
In simple words: Multiply by 100 by appending two zeros to 519.

Exam Tip: Multiplying by powers of 10 just shifts digits to the left.

Question 14. 80 x 900 = ___________.
Answer: 72000
\(8 \times 9 = 72\), add 3 zeros = 72000
In simple words: Multiply 8 and 9, then attach three zeros.

Exam Tip: Total zeros = 1 + 2 = 3 zeros.

Question 15. The product of two numbers does not change even if the ___________ changes.
Answer: order of the numbers
In simple words: Changing factor order does not change the product.

Exam Tip: This is the commutative property of multiplication.

[II] Find the Following Products

Question 1. 769 x 468
Answer: 359892
\(769 \times 8 = 6152\)
\(769 \times 60 = 46140\)
\(769 \times 400 = 307600\)
Sum = \(6152 + 46140 + 307600 = 359892\)
In simple words: Multiply 769 by 8, 60, and 400, then sum the results.

Exam Tip: Double check multi-digit multiplication step by step.

Question 2. 543 x 706
Answer: 383358
\(543 \times 6 = 3258\)
\(543 \times 700 = 380100\)
Sum = \(3258 + 380100 = 383358\)
In simple words: Multiply by 6 and 700, noting the zero in the tens place.

Exam Tip: Skip the tens row since the multiplier digit is 0.

Question 3. 8649 x 863
Answer: 7464087
\(8649 \times 3 = 25947\)
\(8649 \times 60 = 518940\)
\(8649 \times 800 = 6919200\)
Sum = \(25947 + 518940 + 6919200 = 7464087\)
In simple words: Multiply 8649 by 3, 60, and 800 and add together.

Exam Tip: Keep columns precisely aligned to avoid addition errors.

Question 4. 9065 x 397
Answer: 3598805
\(9065 \times 7 = 63455\)
\(9065 \times 90 = 815850\)
\(9065 \times 300 = 2719500\)
Sum = \(63455 + 815850 + 2719500 = 3598805\)
In simple words: Compute partial products for 7, 90, and 300 and sum them.

Exam Tip: Pay attention to zeros inside the multiplicand.

Question 5. 4368 x 579
Answer: 2529072
\(4368 \times 9 = 39312\)
\(4368 \times 70 = 305760\)
\(4368 \times 500 = 2184000\)
Sum = \(39312 + 305760 + 2184000 = 2529072\)
In simple words: Multiply by 9, 70, and 500 and add the partial products.

Exam Tip: Verify carries in every multiplication step.

Question 6. 7096 x 925
Answer: 6563800
\(7096 \times 5 = 35480\)
\(7096 \times 20 = 141920\)
\(7096 \times 900 = 6386400\)
Sum = \(35480 + 141920 + 6386400 = 6563800\)
In simple words: Multiply by 5, 20, and 900, then find the total sum.

Exam Tip: Double check your addition of the large partial products.

[III] Do The Following

Question 1. A notebook contains 180 pages. How many pages are the in 225 such books?
Answer:
Pages in 1 notebook = 180
Number of books = 225
Total pages = \(180 \times 225 = 40500\)
In simple words: Multiply pages per book by total books.

Exam Tip: Include proper units (pages) in your final statement.

Question 2. 2250 bags of sugar were stored in a godown. If each bag contains 25 kg of sugar. Calculate the weight of sugar stored in the godown.
Answer:
Number of bags = 2250
Weight per bag = 25 kg
Total weight = \(2250 \times 25 = 56250 \text{ kg}\)
In simple words: Multiply the number of bags by the weight of each bag.

Exam Tip: Always write units like kg in word problems.

Question 3. There are 2050 students in a school. If each student pays Rs 750 as tuition fee in a month. How much money is collected in a month?
Answer:
Number of students = 2050
Fee per student = Rs 750
Total money collected = \(2050 \times 750 = 1537500\) Rs
In simple words: Multiply students by fee per student.

Exam Tip: Prefix currency unit Rs. correctly.

[IV] Choose the Correct

Question 1. The product of any number and an even number is __________. {even, odd, same number}
(a) even
(b) odd
(c) same number
Answer: (a) even
In simple words: Any integer multiplied by an even number yields an even product.

Exam Tip: Even factor forces the product to be even.

Question 2. The product of two odd numbers is always __________. {odd, even, same number}
(a) odd
(b) even
(c) same number
Answer: (a) odd
In simple words: Multiplying two odd numbers never produces an even number.

Exam Tip: Odd \(\times\) Odd = Odd.

Question 3. 604259 x 0 = __________. {0, 604259, 6042590}
(a) 0
(b) 604259
(c) 6042590
Answer: (a) 0
In simple words: Multiplying any number by 0 gives 0.

Exam Tip: Zero property rules over any large factor.

Question 4. 1 x 764932 = __________. {764932, 1, 1764932}
(a) 764932
(b) 1
(c) 1764932
Answer: (a) 764932
In simple words: Multiplying by 1 leaves the number unchanged.

Exam Tip: Identity property of 1.

Question 5. 20 x 300 = __________. {6000, 600, 2300}
(a) 6000
(b) 600
(c) 2300
Answer: (a) 6000
\(2 \times 3 = 6\), add 3 zeros = 6000
In simple words: Multiply 20 by 300.

Exam Tip: Count total zeros (1 + 2 = 3).

Question 6. 80 x 80 = __________. {160, 6400, 1600}
(a) 160
(b) 6400
(c) 1600
Answer: (b) 6400
\(8 \times 8 = 64\), add 2 zeros = 6400
In simple words: Square of 8 is 64, attach two zeros.

Question 7. 90 x __________ = 3600. {40, 400, 4}
(a) 40
(b) 400
(c) 4
Answer: (a) 40
\(3600 \div 90 = 40\)
In simple words: Divide 3600 by 90 to find the missing factor.

Exam Tip: Cancel one zero from both sides: \(360 \div 9 = 40\).

Unit 5 - Factors and Multiples

[I] Fill In the Blanks

Question 1. A number that has only two factors are called __________ number.
Answer: prime
In simple words: Numbers divisible only by 1 and themselves are prime.

Exam Tip: Prime numbers have exactly two distinct factors.

Question 2. The factors of a prime number __________ and the number itself.
Answer: 1 (one)
In simple words: The only factors of a prime are 1 and itself.

Exam Tip: State the exact factors: 1 and the number.

Question 3. A number that has more than two factors is called __________ number.
Answer: composite
In simple words: Numbers with 3 or more factors are composite.

Exam Tip: Composite numbers can be broken down into prime factor products.

Question 4. __________ has only one factor.
Answer: 1 (One)
In simple words: Number 1 has only one factor (itself).

Exam Tip: 1 is neither prime nor composite because it has only one factor.

Question 5. __________ is neither prime nor composite.
Answer: 1
In simple words: 1 is unique and belongs to neither category.

Exam Tip: Memorize: 1 is neither prime nor composite.

Question 6. The smallest prime number is ___________.
Answer: 2
In simple words: 2 is the first and only even prime number.

Exam Tip: 1 is not prime, so 2 is the smallest prime.

Question 7. The smallest composite number is ___________.
Answer: 4
In simple words: 4 has factors 1, 2, and 4, making it the smallest composite.

Exam Tip: Check factors of 2 (prime), 3 (prime), and 4 (composite).

Question 8. __________ is the only even prime number.
Answer: 2
In simple words: All other even numbers are divisible by 2, hence composite.

Exam Tip: Remember this unique property of 2.

Question 9. All the prime numbers except 2 are ___________.
Answer: odd numbers
In simple words: Every prime number greater than 2 is odd.

Exam Tip: No even number greater than 2 can be prime.

Question 10. Writing a number as a product of its prime factors is known as ___________.
Answer: prime factorization
In simple words: Expressing a composite number using only prime factor multipliers.

Exam Tip: Use factor tree or division method.

Question 11. A number is divisible by 2, if the number is ___________ (or ends in 0, 2, 4, 6, 8).
Answer: even
In simple words: Even numbers end in 0, 2, 4, 6, or 8.

Exam Tip: Check the ones digit for divisibility by 2.

Question 12. A number is divisible by 2, if its one's digit is ___________, ___________, ___________, ___________ or 8.
Answer: 0, 2, 4, 6
In simple words: These are the five even digits.

Exam Tip: List all even single digits.

Question 13. A number is divisible by 5, if its one's digit is ___________ or 5.
Answer: 0
In simple words: Numbers ending in 0 or 5 are divisible by 5.

Exam Tip: Look only at the last digit.

Question 14. A number is divisible by 10, if the one's digit is ___________.
Answer: 0
In simple words: Multiples of 10 always end in zero.

Question 15. A number is divisible by 3, if the ___________ of the digits of the number is divisible by 3.
Answer: sum
In simple words: Add all digits; if the sum is a multiple of 3, the number is divisible by 3.

Exam Tip: Sum rule applies to both 3 and 9.

Question 16. A number is divisible by ___________, if the sum of the digits of the number is divisible by 9.
Answer: 9
In simple words: If digit sum is divisible by 9, the number is divisible by 9.

Exam Tip: If divisible by 9, it is automatically divisible by 3.

[II] Do The Following

Question 1. List the prime numbers between 1 and 50.
Answer:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
In simple words: Numbers between 1 and 50 with exactly two distinct factors.

Exam Tip: Memorize primes up to 50 for quick exam answers.

Question 2. List the composite numbers between 10 and 55.
Answer:
12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54
In simple words: All non-prime numbers (excluding 1) in the range.

Exam Tip: Exclude all prime numbers from the complete list.

Question 3. Circle the prime numbers from the following numbers: 5, 13, 20, 23, 25, 30, 68, 73, 83, 89, 95, 99
Answer:
Prime numbers: 5, 13, 23, 73, 83, 89
In simple words: Identify numbers having only two factors (1 and themselves).

Exam Tip: Check divisibility by 2, 3, 5, 7 to confirm.

Question 4. Underline the composite numbers from the following numbers: 3, 9, 18, 22, 27, 33, 47, 53, 61, 74, 84, 95
Answer:
Composite numbers: 9, 18, 22, 27, 33, 74, 84, 95
In simple words: Highlight numbers having more than two factors.

Exam Tip: Primes in the list (3, 47, 53, 61) should not be underlined.

Question 5. Find the prime factorization of the following numbers by the division method: 25, 36, 40, 55, 60, 76, 82, 95
Answer:
- 25 = \(5 \times 5\)
- 36 = \(2 \times 2 \times 3 \times 3\)
- 40 = \(2 \times 2 \times 2 \times 5\)
- 55 = \(5 \times 11\)
- 60 = \(2 \times 2 \times 3 \times 5\)
- 76 = \(2 \times 2 \times 19\)
- 82 = \(2 \times 41\)
- 95 = \(5 \times 19\)
In simple words: Divide continuously by the smallest possible prime numbers until 1 is reached.

Exam Tip: Always write factors in ascending order.

Question 6. Test each of the following numbers for divisibility: {1} by 3, {2} by 5, {3} by 9 for numbers: 4015, 2745, 30410, 65232, 10624, 42942, 18400, 27063
Answer:
Divisibility by 3 (Sum of digits is multiple of 3):
- 4015: \(4+0+1+5 = 10\) (No)
- 2745: \(2+7+4+5 = 18\) (Yes)
- 30410: \(3+0+4+1+0 = 8\) (No)
- 65232: \(6+5+2+3+2 = 18\) (Yes)
- 10624: \(1+0+6+2+4 = 13\) (No)
- 42942: \(4+2+9+4+2 = 21\) (Yes)
- 18400: \(1+8+4+0+0 = 13\) (No)
- 27063: \(2+7+0+6+3 = 18\) (Yes)

Divisibility by 5 (Ends in 0 or 5):
- 4015: Yes
- 2745: Yes
- 30410: Yes
- 65232: No
- 10624: No
- 42942: No
- 18400: Yes
- 27063: No

Divisibility by 9 (Sum of digits is multiple of 9):
- 4015: No
- 2745: \(18\) (Yes)
- 30410: No
- 65232: \(18\) (Yes)
- 10624: No
- 42942: \(21\) (No)
- 18400: No
- 27063: \(18\) (Yes)
In simple words: Check digit sums for 3 and 9, and the last digit for 5.

Exam Tip: Show addition of digits explicitly to earn full credit.

Question 7. Which of the following numbers are divisible {1} by 2 {2} by 10 for numbers: 71035, 68290, 27451, 90278, 21030, 46130, 72614, 68510
Answer:
Divisible by 2 (Ends in 0, 2, 4, 6, 8):
68290, 90278, 21030, 46130, 72614, 68510

Divisible by 10 (Ends in 0):
68290, 30410 (from list context), 21030, 46130, 68510
In simple words: Divisible by 2 requires an even last digit; divisible by 10 requires a trailing zero.

Exam Tip: All numbers divisible by 10 are also divisible by 2.

[III] Choose the Correct Answer

Question 1. 3 x 2 x 5 is the prime factorization of __________. {30, 325, 35}
(a) 30
(b) 325
(c) 35
Answer: (a) 30
\(3 \times 2 \times 5 = 30\)
In simple words: Multiply the prime factors together.

Exam Tip: Product of prime factors equals the original number.

Question 2. The prime factorization of 26 is __________. {2x2x3x3, 2x2x3, 2x3x3} (Note: option correction to 2 x 13)
Answer: 2 x 13
In simple words: 26 factors into primes 2 and 13.

Exam Tip: Verify prime status of all factors.

Question 3. 365 is divisible by __________. {2, 5, 10}
(a) 2
(b) 5
(c) 10
Answer: (b) 5
In simple words: 365 ends in 5, making it divisible by 5.

Exam Tip: Last digit 5 means divisibility by 5.

Question 4. 47 is a __________ number. {prime, composite, even}
(a) prime
(b) composite
(c) even
Answer: (a) prime
In simple words: 47 has no positive divisors other than 1 and itself.

Exam Tip: Memorize primes up to 50.

Question 5. __________ is neither prime nor composite. {1, 2, 4}
(a) 1
(b) 2
(c) 4
Answer: (a) 1
In simple words: 1 is a unique number with only one factor.

Exam Tip: Frequently asked number theory question.

Question 6. __________ is the greatest 2 digit prime number. {97, 99, 89}
(a) 97
(b) 99
(c) 89
Answer: (a) 97
In simple words: 97 is the largest prime before 100.

Exam Tip: 99 is divisible by 3 and 9; 97 is prime.

Question 7. The prime number just less than 35 is __________. {33, 31, 34}
(a) 33
(b) 31
(c) 34
Answer: (b) 31
In simple words: Counting backward from 35, 31 is prime.

Exam Tip: Check odd numbers below 35.

Question 8. The prime number just greater than 70 is __________. {71, 73, 76}
(a) 71
(b) 73
(c) 76
Answer: (a) 71
In simple words: 71 is the very next prime number after 70.

Question 1. The largest number that is a factor of 2 or more given numbers is known as their __________.
Answer: Highest Common Factor (HCF)
In simple words: HCF is the greatest factor shared by numbers.

Exam Tip: HCF is also called Greatest Common Divisor (GCD).

Question 2. If a number is a factor of 2 given numbers it will be a factor of their __________ as well as their difference.
Answer: sum
In simple words: Common factors divide both the sum and difference of numbers.

Exam Tip: Useful property in number theory.

Question 3. The HCF of 1 and 5 is __________.
Answer: 1
In simple words: 1 shares only 1 as a common factor with any number.

Exam Tip: HCF of 1 and any number is always 1.

Question 4. The HCF of 2 and 4 is __________.
Answer: 2
In simple words: 2 divides both 2 and 4 evenly.

Exam Tip: When a smaller number divides a larger one, the smaller number is their HCF.

Question 5. Every number is a multiple of __________.
Answer: 1 (and itself)
In simple words: 1 divides every integer.

Exam Tip: 1 is a universal factor.

Question 6. Every number is a multiple of __________.
Answer: itself
In simple words: A number multiplied by 1 equals itself.

Exam Tip: Every number is a multiple of 1 and itself.

Question 7. Every multiple of a number is __________ or equal to the number.
Answer: greater than
In simple words: Multiples start at the number itself and increase.

Exam Tip: Multiples \(\ge\) the number; Factors \(\le\) the number.

Question 8. The smallest of the common multiple of 2 or more numbers is called __________.
Answer: Lowest Common Multiple (LCM)
In simple words: LCM is the smallest positive number shared among multiples.

Question 9. LCM of 1 and 7 is __________.
Answer: 7
In simple words: The LCM of 1 and any number is that number.

Exam Tip: LCM with 1 equals the other number.

Question 10. LCM of 2 and 6 is __________.
Answer: 6
In simple words: Since 2 divides 6, the LCM is 6.

Exam Tip: When one number is a multiple of another, the larger number is the LCM.

[II] Find the HCF of the following numbers by division method

Question 1. {1} 35, 50
Answer: 5
\(50 \div 35 = 1\) remainder 15
\(35 \div 15 = 2\) remainder 5
\(15 \div 5 = 3\) remainder 0
HCF = 5
In simple words: Apply long division until remainder is 0.

Exam Tip: The last non-zero divisor is the HCF.

Question 1. {2} 40, 48, 56
Answer: 8
HCF of 40 and 48 = 8
HCF of 8 and 56 = 8
HCF = 8
In simple words: Find HCF of first two numbers, then find HCF of that result with the third number.

Exam Tip: For three numbers, find common factor in stages.

Question 1. {3} 32, 64, 80
Answer: 16
HCF of 32 and 64 = 32
HCF of 32 and 80 = 16
HCF = 16
In simple words: Use division method successively.

Exam Tip: Check if all numbers share a common factor like 16.

Question 1. {4} 44, 55
Answer: 11
\(55 \div 44 = 1\) remainder 11
\(44 \div 11 = 4\) remainder 0
HCF = 11
In simple words: Both numbers are multiples of 11.

Exam Tip: Look for common multiplication tables.

Question 1. {5} 68, 76, 84
Answer: 4
HCF of 68 and 76 = 4
HCF of 4 and 84 = 4
HCF = 4
In simple words: Divide successively to find the greatest common divisor.

Exam Tip: Verify divisibility of all numbers by 4.

Question 1. {6} 48, 64, 72
Answer: 8
HCF of 48 and 64 = 16
HCF of 16 and 72 = 8
HCF = 8
In simple words: Find HCF pairwise.

Exam Tip: Double check division steps.

[III] Find the LCM of the following numbers by division method

Question 1. {1} 77, 84
Answer: 924
Prime factors: \(77 = 7 \times 11\), \(84 = 2^2 \times 3 \times 7\)
LCM = \(4 \times 3 \times 7 \times 11 = 924\)
In simple words: Multiply highest powers of all prime factors.

Exam Tip: Use prime factorization table for large numbers.

Question 1. {2} 60, 70, 80
Answer: 1680
Common division:
2 | 60, 70, 80
2 | 30, 35, 40
5 | 15, 35, 20
   3, 7, 4
LCM = \(2 \times 2 \times 5 \times 3 \times 7 \times 4 = 1680\)
In simple words: Divide all numbers by common prime factors until all quotients are coprime.

Exam Tip: Multiply all divisors and final quotients.

Question 1. {3} 25, 35, 50
Answer: 350
Prime factorizations:
\(25 = 5^2\)
\(35 = 5 \times 7\)
\(50 = 2 \times 5^2\)
LCM = \(2 \times 7 \times 5^2 = 2 \times 7 \times 25 = 350\)
In simple words: Take the highest power of each prime factor (2, 5, 7).

Exam Tip: \(5^2\) is used because it appears in 25 and 50.

Question 1. {4} 36, 48, 72
Answer: 144
\(36 = 2^2 \times 3^2\)
\(48 = 2^4 \times 3\)
\(72 = 2^3 \times 3^2\)
LCM = \(2^4 \times 3^2 = 16 \times 9 = 144\)
In simple words: Take highest exponents of 2 and 3.

Exam Tip: Highest power of 2 is \(2^4\); highest power of 3 is \(3^2\).

Question 1. {5} 28, 56, 96
Answer: 672
\(28 = 2^2 \times 7\)
\(56 = 2^3 \times 7\)
\(96 = 2^5 \times 3\)
LCM = \(2^5 \times 3 \times 7 = 32 \times 3 \times 7 = 672\)
In simple words: Find LCM using prime factorization or common division.

Exam Tip: Always double check multiplication of prime powers.