Question

Find HCF of 65 and 117 and express it in the form 65m+117n

Answer 1

Between 65 and 117; 117 is greater than 65

Division lemma of 117 and 65:

⇒ 117 = 65 x 1 + 52

⇒ 65 = 52 x 1 + 13

⇒ 52 = 4 x 13 + 0

In this step the remainder is zero.

Thus, the divisor i.e. 13 in this step is the H.C.F. of the given numbers

The H.C.F. of 65 and 117 is 13

Now, 13 = 65 – 52 x 1

⇒ 52 = 117 – 65 x 1

⇒ 13 = 65 – (117 – 65 x 1) x 1

⇒ 13 = 65 x 2 – 117

⇒ 13 = 65 x 2 + 117 x (–1)

Therefore H.C.F. of 65 and 117 is of the form 65m + 117n, where m = 2 and n = –1.