Question

find the HCF of 96 and 72 by using the Euclid division Lemma

Answer 1

Hi Friend,

Here is your answer,

96 = 72 × 1 + 24
72 = 24 × 3 + 0

H.C.F= 24


Hope it helps you!

Answer 2

Given: Two numbers-  96 and 72

To find: HCF of given numbers using Euclid's Division Lemma

Solution:

(Definition - According to Euclid's division lemma, if we have two positive integers a and b, then there exist unique integers q an r which satisfies the condition a = bq + r where 0 ≤ r < b)

The larger integer is 96 and smaller is 72

We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers where a = 96 and b = 72.

We get,

⇒ 96 = 72 × 1 + 24

Now, we need to apply Euclid's Division Lemma again taking a = 72 and b = 24

⇒ 72 = 24 × 3 + 0

As the remainder has become 0, we can't proceed further.

Now, the divisor is 24.

Hence, 24 is the HCF of 96 and 72.