If the hcf of 65 and 117 is expressible in the form of 65m - 117,then the value of m is a). 4b.) 2c.) 1d.) 3

By Euclid’s division algorithm:

117 = 65 x 1 + 52 ... (1)
65 = 52 x 1 + 13 ... (2)
52 = 13 x 4 + 0 ... (3)

So HCF of (65, 117) is 13.
Now from equations (1), (2) and (3) we can write: 13 = 65 m 117 => m = 2

Hence, option (b) is correct.

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