Question

Apply Euclid's division algorithm to find HCF of 4052 and 420.

Answer 1

Answer:4052=420×9+272

420=272×1+148

272=148×1+124

148=124×1+24

124=24×5+4

24=4×6+0

HCF is 4

Step-by-step explanation:

Answer 2

Given: Two numbers-  4052 and 420

To find: HCF of given numbers using Euclid's Division Lemma

Solution:

(Definition - According to Euclid's division lemma algorithm, if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b)

The larger integer is 4052 and smaller is 420

We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers where a = 4052 and b = 420.

We get,

⇒ 4052 = 420 × 9 + 272

Now, we need to apply Euclid's Division Lemma again taking a = 420 and b = 272

⇒ 420 = 272 × 1 + 148

Taking a = 272 and b = 148

⇒ 272 = 148 × 1 + 124

Taking a = 148 and b = 124

⇒ 148 = 124 × 1 + 24

Taking a = 124 and b = 24

⇒ 124 = 24 × 5 + 4

Taking a = 24 and b = 4

⇒ 24 = 4 × 6 + 0

As the remainder has become 0, we can't proceed further.

Now, the divisor is 4.

Hence, 4 is the HCF of 4052 and 420.