Question

find the hcf of 36,96,120 by euclid lemma​

Answer 1

Step-by-step explanation:

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.

HOPE THIS WILL HELP YOU....

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Answer 2

Answer:

2×2×3×3 , 2^5×3 , 2^3×3×5

2^2×3=12 hcf