Question

Find the HCF of 65 and 117 and find a Pair of integral values of M and M such that it’s HCF is equal to 65M +117 N

Answer 1

117=65×1+52

65=52×1+13

52=13×4+0

So,13 is the HCF.

117=65×1+52

52=117-65 (1)

65=52×1+13

13=65-52×1

13=65-(117-65) { From 1}

=65-117+65

=2(65)-117 (2)

13=65m-117 (3)

So,from (2) and (3)

m = 2