Question

find HCF of 65 and 117 and Express it in the form of 65 M + 117 m

Answer 1

Hiii friend,


Prime factorisation of 65 = 5 × 13


Prime factorisation of 117 = 3 × 3 × 13


HCF of 65 and 117 = 13


According to question,


65M+117M = 13


182M = 13

M = 13/182 => 1/14.


HOPE IT WILL HELP YOU..... :-)

Answer 2

Hey, here

Sol.

Since 117 > 65
Division lemme of 117 > 65 :

=> 117 = 65 × 1 + 52
=> 65 = 52 × 1 + 13
=> 52= 4 × 13 + 0

In this step the remainder is zero.
Thus, the division 13 in this step in the HCF of the given number

The HCF of 65 and 117 is 13

Now,
$13 = 65 - 52 \times - 1 \\ = >52 = 117 - 65 \times 1 \\ = > 13 = 65 - (117 - 65 \times 1) \times 1 \\ = > 13 = 65 \times 2 - 117 \\ = > 13 = 65 \times 2 + 117x( - 1)$
THEREFORE HCF of 65 and 117 is in the form 65m + 117 m , where

m=2 and m= -1
_____________________________

Hope it's helps you
☺☺