RBSE Solutions Class 5 Maths Chapter 5 Multiples and Factors Important Questions

Question 1. Four multiples of number 3 is-
(a) 3, 7, 9, 14
(b) 3/6, 10, 14
(c) 3,6, 9, 12
(d) 2, 4, 6, 8
Answer: (c) 3,6, 9, 12
In simple words: Multiples are numbers you get when you multiply a number by other whole numbers. The first four multiples of 3 are 3, 6, 9, and 12, which are found by multiplying 3 by 1, 2, 3, and 4 respectively.

🎯 Exam Tip: To find multiples, just multiply the given number by 1, 2, 3, and so on. This will give you its multiples in order.

Question 2. 25,30, 35,40, 45 are the multiples of in the following-
(a) 6
(b) 2
(c) 3
(d) 5
Answer: (d) 5
In simple words: All the numbers listed (25, 30, 35, 40, 45) end in either 0 or 5. This is a special trick to know that they can all be divided by 5 without any remainder.

🎯 Exam Tip: A quick way to identify multiples of 5 is to check if the number ends in 0 or 5.

Question 3. In the following, 16 is the multiple of
(a) 1, 2, 4, 8 and 16
(b) 2, 4 and 10
(c) 3, 4 and 8
(d) 3, 5 and 8
Answer: (a) 1, 2, 4, 8 and 16
In simple words: A number is a multiple of its factors. The numbers 1, 2, 4, 8, and 16 are all factors of 16 because 16 can be divided by each of them exactly.

🎯 Exam Tip: Remember, a number is a multiple of all its factors. Always start by listing factors from 1 up to the number itself.

Question 4. In the following, 40 and 80 are the multiples of-
(a) 5 and 8
(b) 5 and 21
Answer: (a) 5 and 8
In simple words: Both 40 and 80 can be divided evenly by 5 (since they end in 0) and also by 8 (because 5 times 8 is 40 and 10 times 8 is 80). So, 40 and 80 are multiples of both 5 and 8.

🎯 Exam Tip: To check if a number is a multiple of another, perform division. If there is no remainder, it is a multiple.

Question 6. Factors of 6 are-
(a) 1, 3, 6
(b) 3, 6
(c) 1, 2, 3
(d) 1,2, 3,6
Answer: (d) 1,2, 3,6
In simple words: Factors are numbers that divide another number evenly. For the number 6, the numbers 1, 2, 3, and 6 can all divide 6 without leaving any remainder.

🎯 Exam Tip: To find all factors of a number, test division by numbers starting from 1 up to the number itself. If a number divides it evenly, it's a factor.

Question 7. Least common multiple of 5 and 8 is-
(a) 40
(b) 20
(c) 25
(d) 16
Answer: (a) 40
In simple words: The smallest number that is a multiple of both 5 and 8 is 40. You can list the multiples of 5 (5, 10, 15, 20, 25, 30, 35, 40) and multiples of 8 (8, 16, 24, 32, 40) to see that 40 is the first number they share.

🎯 Exam Tip: The least common multiple (LCM) is the smallest positive number that is a multiple of two or more given numbers.

Fill In The Blanks

1. All ___________ of each number are exactly divisible by that number.
Answer: All *factors* of each number are exactly divisible by that number. Factors are numbers that divide another number without a remainder.
In simple words: A number's factors can always divide that number perfectly.

🎯 Exam Tip: Remember, factors divide a number, while multiples are found by multiplying a number.

2. In the table 7, 8th multiple is ___________ .
Answer: In the table 7, the 8th multiple is *56*. This is found by multiplying 7 by 8.
In simple words: To find the 8th multiple of 7, just multiply 7 by 8, which gives 56.

🎯 Exam Tip: Multiples are like counting by a number; the 'nth' multiple is found by multiplying the number by 'n'.

Very Short Answer Type Questions

Question 1. In number chart 1 – 100. Write the multiples of 17.
Answer: The multiples of 17 in the number chart from 1 to 100 are 17, 34, 51, 68, and 85. These are obtained by multiplying 17 by 1, 2, 3, 4, and 5.
In simple words: When you count by 17s up to 100, the numbers you get are 17, 34, 51, 68, and 85.

🎯 Exam Tip: To list multiples within a range, start multiplying the number by whole numbers (1, 2, 3, ...) until the product exceeds the given range.

Question 2. In number chart (1 - 100) write common multiples of 7 and 11.
Answer: To find common multiples of 7 and 11, we first find their least common multiple (LCM). Since 7 and 11 are prime numbers, their LCM is their product, which is \( 7 \times 11 = 77 \).
Therefore, the common multiple of 7 and 11 within the range of 1 to 100 is 77.
In simple words: The only number between 1 and 100 that can be divided by both 7 and 11 is 77. This is because 7 times 11 makes 77.

🎯 Exam Tip: The least common multiple (LCM) of two prime numbers is always their product. All other common multiples will be multiples of this LCM.

Question 3. Find first three even multiples of 5.
Answer: First, list some multiples of 5: 5, 10, 15, 20, 25, 30, 35.
From this list, we identify the even numbers. Even numbers are those that can be divided by 2.
The first three even multiples of 5 are 10, 20, and 30.
In simple words: The multiples of 5 that are also even numbers are 10, 20, and 30. You get them by multiplying 5 by 2, 4, and 6.

🎯 Exam Tip: Even multiples of an odd number are found by multiplying the number by even integers (2, 4, 6, etc.).

Question 4. Find first four odd multiples of 5.
Answer: First, list some multiples of 5: 5, 10, 15, 20, 25, 30, 35.
From this list, we pick the odd numbers. Odd numbers are those that cannot be divided evenly by 2.
The first four odd multiples of 5 are 5, 15, 25, and 35.
In simple words: The multiples of 5 that are also odd numbers are 5, 15, 25, and 35. You get them by multiplying 5 by 1, 3, 5, and 7.

🎯 Exam Tip: Odd multiples of a number are found by multiplying the number by odd integers (1, 3, 5, etc.).

Question 6. Find all factors of 54.
Answer: Factors are numbers that divide 54 completely without leaving a remainder.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. These are the numbers that can be multiplied together to get 54.
In simple words: The numbers that can divide 54 perfectly are 1, 2, 3, 6, 9, 18, 27, and 54.

🎯 Exam Tip: To find all factors, start checking from 1 upwards, forming pairs of numbers that multiply to give the original number. Stop when you start repeating pairs.

Question 7. Find common factors of 27 and 30.
Answer: First, we list the factors for each number:
Factors of 27 are: 1, 3, 9, 27.
Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
Now, we look for numbers that appear in both lists.
The common factors of 27 and 30 are 1 and 3.
In simple words: The numbers that can divide both 27 and 30 perfectly are 1 and 3.

🎯 Exam Tip: Always list all factors for each number first, then clearly identify the ones that are present in every list to find common factors.

Short Answer Type Questions

Question 1. Find the greatest number which divided 15, 45 & 60 completely.
Answer: To find the greatest number that divides 15, 45, and 60 completely, we need to find their Highest Common Factor (HCF).
First, list all factors for each number:
Factors of 15: 1, 3, 5, 15
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors for 15, 45, and 60 are 1, 3, 5, and 15.
The greatest among these common factors is 15.
Therefore, 15 is the highest number which can exactly divide 15, 45, and 60. This is also called the HCF.
In simple words: The biggest number that can divide 15, 45, and 60 evenly is 15. This is because 15 is a factor of all three numbers, and no larger number divides them all.

🎯 Exam Tip: When asked for the "greatest number which divides completely," you are looking for the Highest Common Factor (HCF) of the given numbers.

Question 2. Write first three common multiples of 2 and 5.
Answer: To find the common multiples of 2 and 5, we can list the multiples of each number:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
Now, we identify the numbers that appear in both lists. These are the common multiples.
The first three common multiples of 2 and 5 are 10, 20, and 30. The least common multiple (LCM) of 2 and 5 is 10.
In simple words: The numbers that can be divided by both 2 and 5 are 10, 20, and 30. These are the first few numbers that appear in both the 'times 2' table and the 'times 5' table.

🎯 Exam Tip: The common multiples of two numbers are always multiples of their Least Common Multiple (LCM). For 2 and 5, the LCM is 10, so common multiples are 10, 20, 30, and so on.

Question 4. Find the largest number which exactly divides 20, 40 and 60.
Answer: To find the largest number that exactly divides 20, 40, and 60, we need to find their Highest Common Factor (HCF).
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors of 20, 40, and 60 are 1, 2, 4, 5, 10, and 20.
The highest (largest) among these common factors is 20.
Therefore, 20 is the largest number that can exactly divide 20, 40, and 60.
In simple words: The biggest number that divides 20, 40, and 60 without leaving any remainder is 20. This is because all three numbers are multiples of 20.

🎯 Exam Tip: When looking for the "largest number that divides," you are calculating the HCF. It's often helpful to list factors in pairs to ensure you don't miss any.

Question 5. Write highest factor of number 64.
Answer: The highest factor of any number is always the number itself.
For the number 64, its factors are all the numbers that can divide it evenly. These include 1, 2, 4, 8, 16, 32, and 64.
Among these, the largest factor is 64. A number is always its own greatest factor.
In simple words: The biggest number that can divide 64 evenly is 64 itself. Every number is its own largest factor.

🎯 Exam Tip: Remember two facts about factors: 1 is always the smallest factor of any number, and the number itself is always its largest factor.

Question 6. Write all the factors of 42.
Answer: Factors of 42 are the numbers that divide 42 completely without a remainder.
We can find them by looking for pairs of numbers that multiply to 42:
\( 1 \times 42 = 42 \)
\( 2 \times 21 = 42 \)
\( 3 \times 14 = 42 \)
\( 6 \times 7 = 42 \)
Therefore, all the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
In simple words: The numbers that divide into 42 perfectly are 1, 2, 3, 6, 7, 14, 21, and 42.

🎯 Exam Tip: To list factors systematically, start with 1 and go up, checking each number. Once you reach a factor that has already appeared as the second number in a pair, you have found all unique factors.