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Find the H.C.F of 65 and …

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Find the H.C.F of 65 and 117 and express it in form 65m +117n

Posted by Pragati Jain 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

First find the HCF of 65 and 117 by Using Euclid's division algorithm,
117 = 65{tex}\times{/tex} 1 + 52
65 = 52{tex}\times{/tex} 1 + 13
52 = 13{tex}\times{/tex} 4 + 0
So, HCF of 117 and 65 = 13
HCF = {tex}65m + 117n{/tex}
For, {tex}m= 2{/tex} and {tex}n = -1{/tex},
HCF = 65{tex}\times{/tex} 2 + 117{tex}\times{/tex} (-1)
= 130 - 117
= 13
Hence, the integral values of m and n are 2 and -1 respectively and the HCF of 117 and 65 is 13.

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CBSE > Class 10 > Mathematics