Question

find the hcf of no 72 & 96 by euclid division algorithm and express it in the form 96m+72n where m and n are some integers.

Answer 1

Hi ,
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Euclid's Division Lemma :

Given positive integers a and b ,

there exists unique integers q and r

satisfying

a = bq + r ,

Where 0 less than or equal to r
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Applying Euclid's Division algorithm

to 72 and 96 , we get

96 = 72 × 1 + 24 ----( 1 )

72 = 24 × 3 + 0 -----( 2 )

Therefore 24 is the HCF of 72 and 96

From ( 1 ),

24 = 96 - 72 × 1

= 96 ( 1 ) + 72 × ( - 1 )

It is in the form of

= 96m + 72n

I hope this helps you.

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Answer 2

HCF (96 & 72) = 96 = 72 *1 + 24
72 = 24 * 3 + 0
therefore HCF is 24...