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Find HCF of 65 and 117 …

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Find HCF of 65 and 117 and find a pair of integral values of m&n such that HCF =65m+117n.

Posted by Nikita Sharma 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 10 months ago

<font face="Arial, sans-serif"><font style="box-sizing: inherit; outline: none; user-select: initial !important; max-width: 100%; overflow: hidden;">By Euclid's division algorithm

117 = 65x1 + 52.</font></font>

65 = 52x1 + 13

52 = 13x4 + 0

Therefore 13 is the HCF (65, 117).

Now work backwards:

13 = 65 + 52x(-1)

13 = 65 + [117 + 65x(-1)]x(-1)

13 = 65x(2) + 117x(-1).

∴ m = 2 and n = -1.

3Thank You

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