CBSE Class 5 Mathematics Be My Multiple Worksheet Set 04

Question 1. Find out the common factors of the following numbers.
a) 16, 48
Answer: Factors of 16 = 1, 2, 4, 8, 16
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors of 16 and 48 = 1, 2, 4, 8, 16
In simple words: The numbers that divide both 16 and 18 without leaving a remainder are 1, 2, 4, 8, and 16.
Exam Tip: Always list factors in pairs (e.g., \(1 \times 16\), \(2 \times 8\), \(4 \times 4\)) so you do not miss any numbers.

Question 1 (b). Find out the common factors of the following numbers: 10, 15, 35
Answer: Factors of 10 = 1, 2, 5, 10
Factors of 15 = 1, 3, 5, 15
Factors of 35 = 1, 5, 7, 35
Common factors of 10, 15, and 35 = 1, 5
In simple words: The only numbers that divide all three numbers completely are 1 and 5.

Exam Tip: When finding common factors for three numbers, check if the smallest number's factors divide the other two numbers.

Question 1 (c). Find out the common factors of the following numbers: 36, 45
Answer: Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 45 = 1, 3, 5, 9, 15, 45
Common factors of 36 and 45 = 1, 3, 9
In simple words: The shared factors present in both lists are 1, 3, and 9.

Exam Tip: The highest common factor (HCF) here is 9, which means all common factors must be divisors of 9.

Question 1 (d). Find out the common factors of the following numbers: 12, 120
Answer: Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Common factors of 12 and 120 = 1, 2, 3, 4, 6, 12
In simple words: Since 120 is a multiple of 12, all factors of 12 are also common factors.

Exam Tip: If one number is a multiple of the other, the smaller number and its factors are automatically the common factors.

Question 2. Write the common multiple of the following numbers.
a) 16, 42, 24
Answer: Multiples of 16 = 16, 32, 48, ..., 336, ...
Multiples of 42 = 42, 84, 126, 168, ..., 336, ...
Multiples of 24 = 24, 48, 72, ..., 336, ...
Least Common Multiple (LCM) and first common multiple = 336
Other common multiples = 672, 1008, and so on.
In simple words: The first number that appears in the multiplication tables of 16, 42, and 24 is 336.

Exam Tip: For large numbers, find the LCM using prime factorization to save time instead of writing out long lists of multiples.

Question 2 (b). Write the common multiple of the following numbers: 60, 36
Answer: Multiples of 60 = 60, 120, 180, 240, 300, ...
Multiples of 36 = 36, 72, 108, 144, 180, 216, ...
First common multiple (LCM) of 60 and 36 = 180
Other common multiples = 360, 540, and so on.
In simple words: 180 is the smallest number that is a multiple of both 60 and 36.

Exam Tip: You can find the first common multiple by listing multiples of the larger number (60) and checking which one divides evenly by the smaller number (36).