Question

Using Euclid’s division algorithm, find the HCF of 250, 175 and 425.

Answer 1

Given numbers are 250, 175 and 425

∴ 425 > 250 > 175

On applying Euclid’s division lemma for 425 and 250, we get

425 = 250 × 1 + 175

Here, r = 175 ≠ 0.

So, again applying Euclid’s division lemma with new dividend 250 and new divisor 175, we get

250 = 175 × 1 + 75

Here, r = 75 ≠ 0

So, on taking 175 as dividend and 75 as the divisor and again we apply Euclid’s division lemma, we get

175 = 75 × 2 + 25

Here, r = 25 ≠ 0.

So, again applying Euclid’s division lemma with new dividend 75 and new divisor 25, we get

75 = 25 × 3 + 0

Here, r = 0 and divisor is 25.

So, HCF of 425 and 225 is 25.

Now, applying Euclid’s division lemma for 175 and 25, we get

175 = 25 × 7 + 0

Here, remainder = 0

So, HCF of 250, 175 and 425 is 25.