Question

use Euclid division lemma to find hcf of 4056 and 12576​

Answer 1

To Find:-

HCF of 4056 & 12576

Analysis,

We have to find the HCF of 4056 and 12576 by Euclids Division Lemma.Divide it until we get tthe remainder as 0.

Concept Used:-

According to Euclid’s Division Lemma 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.HCF is the largest number which exactly divides two or more positive integers.

Solution:-

12576 = (4052 × 3) + 420

Now we have to consider the new divisor 4052 and the new remainder 420.Then,apply the same procedure.

4052 = (420 × 9) + 272

Consider the new divisor 272 and the new remainder 148.

272 = (148 × 1) + 124

Consider the new divisor 148 and the new remainder 124.

148 = (124 × 1) + 24

Consider the new divisor 124 and the new remainder 24.

124 = (24 × 5) + 4

Consider the new divisor 24 and the new remainder 4.

24 = (4 × 6) + 0

Hence,

HCF of (4056,12576) = 4

Answer 2

$\:$

12576 = 4052×3+420

4052= 420×9+272

420 = 272×1+148

148 = 124× 1+124

124 = 24×5+4

24 = 4×6+0

H.C.F of 12576 and 4052 = 4