Question

Find the HCF of 65 and 117 . Write it in terms of 65m+117n.

Answer 1

Using Euclid's Division Lemma :

117 = 65 * 1 + 52 => ( Equation 1 )

65 = 52 * 1 + 13 => ( Equation 2 )

52 = 13 * 4 + 0

Hence 13 is the HCF of 65 and 117.

13 = 65 m + 117 n

From Equation 2 we can say that,

13 = 65 - 52 * 1 => ( Equation 3 )

From Equation 1 we can say that,

52 = 117 - 65 * 1 => Equation 4

Substituting the value of 52 as in Equation 3 in Equation 4. We get,

13 = 65 - ( 117 - 65 * 1 )

13 = 65 + 65 - 117

13 = 65 * 2 + 117 * ( - 1 )

13 = 65 m + 117 n

=> m = 2 ; n = ( - 1 )