If HCF of 65 and 117 can be expressed in the form 65m+117n, find the value of m and n.
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.