Question

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

Answer 1

Hii Pavan,

● Answer -

13 = 65×2 + 117×(-1)

● Explanation -

Let's first see factors of 65 & 117,

Factors of 65 = 1, 5, 13, 65

Factors of 117 = 1, 3, 9, 13, 39, 117

From this, we can say that highest common factor of 65 & 117 is 13.

Now, to express it as 65m + 117n.

13 = 65m + 117n

13 = 13×5m + 13×9n

1 = 5m + 9n

As 5m+9n = 1 is a linear equation, it can have multiple solutions. We'll take m = 2 & n = -1.

Hence,

13 = 65×2 + 117×(-1)

Hope this is useful...