Question

find hcf of 65 and 117 and express in form of 65m +117n

Answer 1

 65 = 13 * 5        117 = 3 * 3 * 13

H C F =   65 m +  117 n  =  13
                   or   5 m + 9 n   =  1   

Answer 2

H.C.F. OF 65 & 117 can be found by using Prime Factorization Method:

65 = 13 × 5
117 = 13 × 3 × 3

Hence, their H.C.F. is 13.

13 = 65m + 117n
Dividing by 13 on both the sides,
We get,
13/13 = 65m/13 + 117n/13
1 = 5m + 9n