Question

Find HCF using euclid's division
231 and 396

Answer 1

By Euclid’s division Algorithm,

396 = 231 x 1 + 165

231 = 165 x 1 + 66

165 = 66 x 2 + 33

66 = 33 x 2 + 0

Therefore, HCF of 231 and 96 is = 33

Answer 2

Given:

Two numbers are 231 and 396.

To Find:

The HCF of 231, and 396 by using Euclid’s division method.

Solution:

1. Consider two numbers a and b (a>b). The Euclid division follows the format a = b(q) + r. where q, r is the quotient and remainder respectively when a is divided by b.

2. If r is a non-zero value, b = r(x) + y where x, y is the quotient and remainder respectively when b is divided by x. Keep on using the method till the remainder is 0.  

3. When the remainder is 0, the divisor of that particular step is considered as the HCF.

4. Using the property mentioned above the HCF of 231, and 396 can be calculated,

= > 396 = 231 (1) + 165,

= > 231 = 165 (1) + 66,

= > 165 = 66(2) + 33,

= > 66 = 33(2) + 0.

5. Therefore, HCF is 33.

Therefore, the HCF of 396, 231 is 33.