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

210, 55

From the integers given in the question 210 and 55, it is observed that 210 > 55. So by Euclid’s Division Lemma we get the following:

210 = 55 × 3 + 45

Her the remainder is 45 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 55 and remainder 45.

55 = 45 × 1 + 10

Here the remainder is 10 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 45 and remainder 10.

45 = 10 × 4 + 5

Here the remainder is 5 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 10 and remainder 5.

10 = 5 × 2 + 0

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

So the HCF of 210 and 55 is 5.

The entire process can be expressed in the following way: