1.

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

Answer»

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 )


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