Find the HCF (Highest Common Factor) of the following pairs of number by Euclid Division Algorithm:

135, 225

From the integers given in the question 225 and 135, it is observed that 225 > 135. So by Euclid’s Division Lemma we get the following:

225 = 135 × 1 + 90

Here the remainder is 90 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 135 and remainder 90.

135 = 90 × 1 + 45

Here the remainder is 45 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 90 and remainder 45.

90 = 45 × 2 + 0

So from the above relation is seen that remainder zero is obtained.

So the HCF of 135 and 225 is 45.

The entire process can be expressed in the following way: