Find the HCF of 55 and 210 . express it as a linear combinaton of 55 and 210, i.e. HCF of 55 and 210= 210a +55b, for some a andb

Explanation

First we will find the H.C.F. of 210 and 55.
Here , `210 gt 55`

`therefore " " 210 = 55 xx 3 + 45`
`55 = 45 xx 1 + 10`
`45 = 10 xx 4 +5`
`10 = 5 xx 2 + 0`
Since remainder = 0 `implies " "` recent divisor is the H.C.F.
`therefore` H.C.F. of (210 , 55) = 5
Now, `210 xx 5 + 55x = 5`
`implies " " 55x = 5 - 210 xx 5 = 5- 1050 = - 1045`
`implies " " x = -(1045)/(55) = -19`