Question

Find the h.c.f of 455 and 42 by Euclid's division algorithm?

Answer 1

Here is the answer to your question

Answer 2

We know that

According to Euclid's Division Lemma

Dividend = Divisor × Quotient + Reminder, we will apply division till Remainder comes as zero.

Here 455 > 42, applying Division Lemma on 455 and 42 we get

455 = 42 × 1 + 35

∵ Remainder ≠ 0, applying division lemma on 42 and 35, we get

42 = 35 × 1 + 7

∴ Remainder ≠ 0, applying division lemma on 35 and 7, we get

35 = 7 × 5 + 0

Here Remainder = 0 ∴ Divisor in this step will be HCF of 455 and 42

∴ HCF ( 455, 42) = 7