Using Euclid’s division algorithm, find the HCF of

455 and 42

Given numbers are 455 and 42

Here, 455 > 42

So, we divide 455 by 42

By using Euclid’s division lemma, we get

455 = 42 × 10 + 35

Here, r = 35 ≠ 0.

On taking 42 as dividend and 35 as the divisor and we apply Euclid’s division lemma, we get

42 = 35 × 1 + 7

Here, r = 7 ≠ 0

So, on taking 35 as dividend and 7 as the divisor and again we apply Euclid’s division lemma, we get

35 = 7 × 5 + 0

The remainder has now become 0, so our procedure stops. Since the divisor at this last stage is 7, the HCF of 455 and 42 is 7.