Find the HCF of 81 and 675 using Euclid's Division Algorithm.

The larger integer is 675, therefore, by applying the Division Lemma a = bq + r, where 0 ≤ r < b.

We have, a = 675 and b = 81

675 = 81 × 8 + 27

Applying Euclid’s Division Algorithm again we have,

81 = 27 × 3 + 0

We cannot proceed further as the remainder becomes zero.

According to the algorithm, in this case, the divisor is 27.

Hence, the HCF of 675 and 81 is 27.