Question

apply Euclid's division algorithm to find HCF of 4052 &420

Answer 1

Given numbers,

4052 and 420

To find,

HCF of 4052 and 420.

By using,

Euclid's division algorithm to 4052 and 420.

Since, 4052 > 420, therefore, applying Euclid's division lemma to 4052 and 420, we get,

4052 = 420 $\times$ 9 + 272

Since, r ≠ 0. So, applying Euclid's division lemma to 420 and 272.

420 = 272 $\times$ 1 + 148

Since, r ≠ 0. So, applying Euclid's division lemma to 272 and 148.

272 = 148 $\times$ 1 + 124

Since, r ≠ 0. So, applying Euclid's division lemma to 148 and 124.

148 = 124 $\times$ 1 + 24

Since, r ≠ 0. So, applying Euclid's division lemma to 124 and 24,

124 = 24 $\times$ 5 + 4

Since, r ≠ 0. So, applying Euclid's division lemma to 24 and 4,

24 = 4 $\times$ 6 + 0

Since, r = 0, the divisor of the last step will be the HCF of given any two numbers.

$\fbox{\bold{\mathsf{\therefore</p><p></p><p>HCF(4052,420)\:is\:4.}}}$

Answer 2

Answer:

HCF = 4

Step-by-step explanation:

Given,

4052,420

a,b are any two positive integers , there exists a unique pair of integers q and r satisfying a=bq +r,0</=r<b,q is not equal to 0

a = 4052 b = 420

a=bq +r

4052 = 420 x 9 + 272

420 = 272 x 1 + 148

272 = 148 x 1 + 124

148 = 124 x 1 + 24

124 = 24 x 5 + 4

24 = 4 x 6 + 0

therefore , HCF of 4052 and 420 = 4