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

420, 130

From the integers given in the question 420 and 130, it is observed that 420 > 130. So by Euclid’s Division Lemma we get the following:

420 = 130 × 3 + 30

Here the remainder is 30 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 130 and remainder 30.

130 = 30 × 4 + 10

Her the remainder is 10 which is not equal to zero. So applying Euclid’s Division Lemma on divisor 30 and remainder 10.

30 = 10 × 3 + 0

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

So the HCF of 420 and 130 is 10.

The entire process can be expressed in the following way: