Question

Find hcf of 65 and 117 and find the pair of integer value of m and n such that hcf= 65m + 117n

Answer 1

117=65*1+52

65=52*1+13

52=13*4+0

13 is the hcf

13=65-52*1

13=65-117+65

13=2*65+117*-1

M=2 n=-1

Answer 2

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Secondary School Cbse board x 15+8 pts

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

by Nikhildcruz3454 17.04.2018

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Safwaan127

Safwaan127Expert

By Euclid's division algorithm

117 = 65x1 + 52.

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.

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