CBSE Class 5 Mathematics Factors And Multiples Worksheet Set 01

Question. The smallest multiple (other than zero) that two or more numbers have in common.
For example: the multiples of 3 are 3, 6, 9, 12, 15.... and the multiples of 5 are 5, 10, 15, 20..... The smallest multiple that both 3 and 5 have in common is 15.
(a) Least Common Multiple
(b) Least Common Factor
(c) Largest Common Multiple
(d) Largest Common Factor
Answer : A

Question. A positive number that is divisible only by itself and the number one. For example:
3 has only two factors - one and three - one and itself.
(a) Prime Number
(b) Composite Number
(c) Factor Number
(d) Addend Number
Answer : A

Question. What is the largest factor that two or more numbers have in common. For example:
The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12 The largest factor that both 8 and 12 have is the number - 4. Four is the largest number both 8 and 12 have in common.
(a) GCF - Greatest Common Factor
(b) LCF - Least Common Factor
(c) GCM - Greatest Common Multiple
(d) LCM - Least Common Multiple
Answer : A

Question. Which of the following best defines the properties of a composite number?
(a) It has more than 2 factors.
(b) It has only 2 factors, one and itself.
(c) It has more than 2 multiples.
(d) It has only 2 multiples.
Answer : A

Question. Which list shows all the prime numbers between 1 to 50 
(a) 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
(b) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
(c) 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
(d) 2, 5, 7, 11, 21, 17, 19, 23, 29, 37, 43, 47
Answer : B

Question. Beginning at 8:30 am, the Calgary Zoo starts tours of the tiger and elephant enclosures. Tours for the tiger enclosure leave every 15 minutes. Tours of the elephant enclosure leave every 20 minutes. How often do the tours leave at the same time?
(a) Every 15 minutes
(b) Every 45 minutes
(c) Every 60 minutes
(d) Every 50 minutes
Answer : C

Question. Bhushan counted to 60 using multiples of 6. Which statement is true about multiples of 6?
(a) They are all odd numbers
(b) They all have 6 in the ones place
(c) They can all be divided evenly by 3
(d) They can all be divided evenly by 12
Answer : C

Question. Read the statements and choose the correct option. 
Statement A: If a number can only be divided by one and itself, it is a prime number.
Statement B: Prime number has only 2 factors, one and itself.
(a) Only statement A is correct.
(b) Only statement B is correct.
(c) Both the statements are correct
(d) Both the statement are wrong.
Answer : C

Question. A number which is a factor of every number is :
(a) 0
(b) 1
(c) 2
(d) 5
Answer : B

Question. Rohan asked a question to Shruti.
“Multiply the second multiple of 12 by the third multiple of 8”.
Help her in solving the question and finding the correct result.
(a) 48
(b) 96
(c) 192
(d) 576
Answer : D

Question. ……. are the numbers which are multiplied together to get another number.
a. Factors.
b. Multiples
c. product
d. sum
Answer : A

Question. Which of the following are two consecutive prime numbers that differ by 2?
a. Co- prime
b. Prime numbers
c. Twin prime
d. composite numbers
Answer : C

Question. Identify the numbers with only 1 as the common factor.
a. Co prime.
b. Twin prime.
c. Composite
d. prime
Answer : A

Question. What are the common factors of 9 and 36?
a. 1,3,9.
b. 1,3,4,9.
C. 1,3,6,9
Answer : A

Question. Find the smallest whole number that is divisible by 10 and 12.
a. 30.
b. 40.
c. 60
d. 70
Answer : C

Question. What is the LCM of two co prime numbers?
a. Their difference
b. Their product
c. Their sum
Answer : B

Question. How many prime numbers are there from 50 to 100?
a. 18.
b. 12.
c. 10
d .50
Answer : C

Question. What is the sum of first five multiples of 8?
a. 120.
b . 90.
c . 100
d. 120
Answer : A

Question. The factor of any number are------- the numbers.
a. Equal to or less than.
b. equal to or greater than
c . Equal to
Answer : A

Question. Fill in the smallest digit to make the number divisible by 6. 9_52
a. 0.
b . 1.
C. 2
d. 8
Answer : C

Question. Fill in the smallest digit to make the number divisible by 4. 104_2
a. 0.
b . 1.
c. 2
d.4
Answer : B

Question. Which of these numbers is divisible by 2 but not by 6.
a. 234.
b .7016.
c. 25314
d.23457
Answer : B

Question. 1170 is not divisible by
a. 10
b . 9.
C 4
Answer : C

Question. A number is divisible by 24 if….
a. It is divisible by 6 and 4 both
b. It is divisible by 8 and 3 both
c. Both are correct.
Answer : B

Question. In how many different ways we can arrange 24 glasses on a kitchen shelf? Choose the best answer.
a. 4 ways ,all 24 glasses in one row. 2rows of 12 glasses each. 3 rows of 8 glasses each. 4 rows of 6glasses each.
b. 3 ways ,all glasses in one row. 2 rows of 12 glasses each. 3 rows of 8 glasses each.
c. 2 ways ,all glasses in one row. 3 rows of 8 glasses each. 4 rows of 6 glasses each.
Answer : A

Find the HCF and LCM of the following. Then match the letter next to the answer to the numbers below.

Question 1. 10, 16
\(10 = 2 \times 5\)
\(16 = 2 \times 2 \times 2 \times 2\)
\(\text{HCF} = 2\) [Box letter: M]
\(\text{LCM} = 80\) [Box letter: T]
Answer: HCF = 2, LCM = 80
In simple words: The greatest common factor of 10 and 16 is 2, and their least common multiple is 80.

Exam Tip: Always write prime factorizations in exponential or expanded form to avoid missing common factors.

Question 2. 12, 18
\(12 = 2 \times 2 \times 3\)
\(18 = 2 \times 3 \times 3\)
\(\text{HCF} = 2 \times 3 = 6\) [Box letter: G]
\(\text{LCM} = 2 \times 2 \times 3 \times 3 = 36\) [Box letter: O]
Answer: HCF = 6, LCM = 36
In simple words: The HCF of 12 and 18 is 6, and their LCM is 36.

Exam Tip: Use prime factorisation or continuous division to quickly find HCF and LCM for small numbers.

Question 3. 9, 21
\(9 = 3 \times 3\)
\(21 = 3 \times 7\)
\(\text{HCF} = 3\) [Box letter: A]
\(\text{LCM} = 3 \times 3 \times 7 = 63\) [Box letter: E]
Answer: HCF = 3, LCM = 63
In simple words: The greatest common factor of 9 and 21 is 3, and their least common multiple is 63.

Exam Tip: Verify your LCM by checking if it is divisible by both given numbers.

Question 4. 20, 45
\(20 = 2 \times 2 \times 5\)
\(45 = 3 \times 3 \times 5\)
\(\text{HCF} = 5\) [Box letter: G]
\(\text{LCM} = 2 \times 2 \times 3 \times 3 \times 5 = 180\) [Box letter: U]
Answer: HCF = 5, LCM = 180
In simple words: The HCF of 20 and 45 is 5, and their LCM is 180.

Exam Tip: Product of two numbers equals the product of their HCF and LCM (\(a \times b = \text{HCF} \times \text{LCM}\)).

Question 5. 18, 54
\(18 = 2 \times 3 \times 3\)
\(54 = 2 \times 3 \times 3 \times 3\)
\(\text{HCF} = 2 \times 3 \times 3 = 18\) [Box letter: C]
\(\text{LCM} = 2 \times 3 \times 3 \times 3 = 54\) [Box letter: O]
Answer: HCF = 18, LCM = 54
In simple words: Since 54 is a multiple of 18, the HCF is 18 and the LCM is 54.

Exam Tip: If the larger number is a multiple of the smaller number, the smaller number is the HCF and the larger number is the LCM.

Question 6. 24, 32
\(24 = 2 \times 2 \times 2 \times 3\)
\(32 = 2 \times 2 \times 2 \times 2 \times 2\)
\(\text{HCF} = 2 \times 2 \times 2 = 8\) [Box letter: N]
\(\text{LCM} = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 96\) [Box letter: T]
Answer: HCF = 8, LCM = 96
In simple words: The greatest common divisor of 24 and 32 is 8, and their lowest common multiple is 96.

Question 7. 35, 27
\(35 = 5 \times 7\)
\(27 = 3 \times 3 \times 3\)
\(\text{HCF} = 1\) [Box letter: I]
\(\text{LCM} = 3 \times 3 \times 3 \times 5 \times 7 = 945\) [Box letter: N]
Answer: HCF = 1, LCM = 945
In simple words: Since 35 and 27 share no common factors other than 1, their HCF is 1 and their LCM is their product.

Exam Tip: Co-prime numbers always have an HCF of 1 and an LCM equal to their product.

Question 8. 81, 63
\(81 = 3 \times 3 \times 3 \times 3\)
\(63 = 3 \times 3 \times 7\)
\(\text{HCF} = 3 \times 3 = 9\) [Box letter: R]
\(\text{LCM} = 3 \times 3 \times 3 \times 3 \times 7 = 567\) [Box letter: A]
Answer: HCF = 9, LCM = 567
In simple words: The HCF of 81 and 63 is 9, and their LCM is 567.

Exam Tip: Double-check prime factor counts when dealing with numbers having repeated prime factors like 81.

Question 9. 92, 69
\(92 = 2 \times 2 \times 23 = 4 \times 23\)
\(69 = 3 \times 23\)
\(\text{HCF} = 23\) [Box letter: T]
\(\text{LCM} = 2 \times 2 \times 3 \times 23 = 276\) [Box letter: F]
Answer: HCF = 23, LCM = 276
In simple words: The HCF of 92 and 69 is 23, and their LCM is 276.

Exam Tip: Memorize prime numbers up to 30 (like 23) to quickly factorize numbers ending in unusual digits.