Question

use euclid s division algorithm to find the hcf of 135 and 225

Answer 1

let 225 = a, and 135 = b 
therefore, by applying the relation a=bq + r,             
where 0≤r<b 
we get,
225 = 135 * 1+ 90  (where,r =90)

Since, r (remainder) is not equal to zero (0).
Thus, by applying the Euclid’s division algorithm,
by taking 135 = a, and 90 = b
we get,
135= 90*1+45  where r= 45
Since, in this step also, r is not equal to zero(0).
 Thus by continuing the Euclid’s division algorithm, by taking this time,
 90 = a, and 45 = b
we get,
90= 45* 2 +0 ( in ths stp we get r = 0)
Therefore, 45 is the HCF of given pair 225 and 135

Thus, Answer: 45