Question

Find the HCF of 36, 96 and 120 by Euclid’s Lemma.

Answer 1

Euclid's division algorithm is a technique to compute the Highest Common Factor (HCF) of two or three given positive integers.
Euclid's division Lemma states that for any two positive integers say a and b there exist two unique whole numbers say q and r ,such that, a = bq+r, where 0≤r<b.

SOLUTION:
On applying euclid's division Lemma for 36 and 96
96 = 36 ×2 + 24
Here, Remainder = 24≠0
So take new Dividend as 36 and divisor as 24.

36 = 24×1 +12
Here, Remainder = 12≠0
So take new Dividend as 24 and divisor as 12.

24 = 12×2 +0
Here, the Remainder = 0 and the last divisor is 12.
So, HCF of 36 and 96 is 12.

On applying euclid's division Lemma for 12 and 120

120 = 12 ×10 + 0

Here Remainder = 0

So , HCF of  36, 96 and 120 is 12.

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