Question

PRACTICE EXERCISE 4.2
For each of the following, find the HCF by using the prime factorisation me
(i) 18,24
(ii) 40, 48, 72
(iii) 72, 144, 252
(iv) 225, 1125,5625
(v) 32, 64,96, 160
(vi) 126, 154, 182, 252
) For each of the following, find the HCF by using the long division metho
(i) 882, 3150
(ii) 1095, 3942
272, 425
(iv) 345, 506​

Answer 1

Step I:

Find the prime factorization of each of the given numbers.

Step II:

The product of all common prime factors is the HCF of the given numbers.

Let us consider some of the examples to find highest common factor by using prime factorization method.

1. Find highest common factor (HCF) of 14 and 8 by using prime factorization method.

Solution:

14 = 1 × 2 × 7.

8 = 1 × 2 × 2 × 2.

Common factor of 8 and 14 = 1 and 2.

H.C.F. is the product of lowest powers of factors common to all numbers.

Highest common factor of 8 and 14 = 2.