Question

if the Hcf of 65 and 117 is expressible in the form of 65m-117 then find the value of m​

Answer 1

$\huge{\mathfrak{\underline{\green{AnSwEr}}}}$

HCF of 65 and 117 by using Euclid division algorithm ;

↦117 = 65×1+52[r≠0]

↦65 = 52×1+13[r≠0] --------(eq.1)

↦52 = 13×4+0[r=0]

So the HCF is 13 ; and it can be expressed as

13 = 65-52×1 [from eq.1]

Now;

↦13 = 65 - (117-65×1)

↦13 = 65 - 117 +65×1

↦13 = 65×2 +117×{-1}

↦13 = 65m +117n

From this ;

Value of m = 2, n= -1