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Find HCF 65 and 117and express it in the...

Find HCF 65 and 117and express it in the form of 65m+117n.

Text Solution

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Here , `117 gt 65`
`therefore`

`therefore " " 117 = 65 xx 1 + 52`
`65 = 52 xx 1 + 13`
`52 = 13 xx 4 + 0`
Since remainder = 0 `" "` recent divisor is the H.C.F.
`therefore` H.C.F. (117, 65) = 13
Now , `" " 13 = 65 - 52 xx 1`
`implies " " 13 = 65 - (117 - 65 xx1)`
= `65 - 117 + 65 xx1`
`= 65 xx 2 - 117`
=65x + 117 y
where , x= 2 and y = `-1`
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