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A number is divisible by both 5 and 12. By which other number will that number be always divisible?

Solution:

We use the concepts of factors and coprime numbers to answer the given question.

We need to find out which number is divisible by both 5 and 12. Since the unknown number is divisible by both 5 and 12, let us find the factors of 5 and 12.

Factors of 5 are 1 and 5

Factors of 12 are 1, 2, 3, 4, 6 and 12.

Since the common factor of these numbers is 1, the given two numbers are co-prime.

Therefore, the number will also be divisible by their product which is 5 x 12 = 60 since if we divide 60 by 5 we get 12 and if we divide 60 by 12, we get 5.

Therefore, the required number is 60.

The number will also be divisible by all the factors of 60.

The factors of 60 are 1,2,3,4,5,6,10,12,15,20,30 and 60.

Therefore, the number will also be divisible by 1,2,3,4,6,10,15,20,30 and 60.

NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.4 Question 6

A number is divisible by both 5 and 12. By which other numbers will that number be always divisible?

Summary:

Using the concepts of factors and coprime numbers, it can be concluded that the required number which is divisible by both 5 and 12 is 60. This number is always divisible by 1,2,3,4,5,6,10,12,15,20,30 and 60.

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