Question

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

Answer 1

Step-by-step explanation:

By Euclid's division algorithm

117=65×1+52→(1)

65=52×1+13→(2)

52=13×4+0→(3)

Therefore 13 is HCF f (65,117)

Now going backward

13=65+52×(−1)

13=65+[117−65×1]×(−1)

[From (1)]

13=65×2+117×(−1)

∴m=2n=−1