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

1.	Find the H.C.F of 65 and 117 and express it in form 65m +117n
Answer» First find the HCF of 65 and 117 by Using Euclid\'s division algorithm,117 = 65{tex}\\times{/tex} 1 + 5265 = 52{tex}\\times{/tex} 1 + 1352 = 13{tex}\\times{/tex} 4 + 0So, HCF of 117 and 65 = 13HCF = {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= 13Hence, the integral values of m and\xa0n are 2 and -1 respectively and the HCF of 117 and 65 is 13.

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