Using Euclid's algorithm, find the HCF of 156 and 504.

Given :

The given numbers are 156 and 504.

To find :

We have to find the HCF of the given numbers by using Euclid's division lemma.

Solution :

By Euclid's division lemma,

$$Dividend = Divisor \times Quotient + Remainder$$ 

Here, $504 > 156$.

So, divide 504 by 156.

$504 = 156 \times 3 + 36$

Remainder $= 36$.

Repeat the above process until we will get 0 as the remainder.

Consider 156 as the dividend and 36 as the divisor, 

$156 = 36 \times 4 +12$

Remainder $= 12$

Consider 36 as the dividend and 12 as the divisor,

$36 = 12 \times 3 + 0$

Remainder $= 0$.

Therefore,

Highest Common Factor of 504 and 156 is 12.