Question

# If the H.C.F of 210 and 55 is expressible in the form 210 x 5 + 55y, find y.

Solution

Let us first find the H.C.F. of 210 and 55.
Applying Euclid's division lemma on 210 and 55, we get
210=55x3+
45 N ..... (i)
Since, the remainder 45+0. So, we now apply division lemma
on the divisor 55 and the remainder 45 to get
55=45 x 1 + 10
..... (ii)
We consider the divisor 45 and the remainder 10 and apply
division lemma to get