Use Euclid's division algorithm

Solution:

Here we have to find the HCF of the numbers 10224 and 9648 by using Euclid’s division algorithm.

We know that If we divide a by b and r is the remainder and q is the quotient, Euclid’s Lemma says that

$A=b q+r$, where $0 \leq r

And HCF of (a, b) = HCF of (b, r)

Here $a=10224$ and $b=9648$

Therefore, we have the following procedure,

$10224=9648 \times 1+576$

Now, we apply the division algorithm on 9648 and 576.

$9648=576 \times 16+432$

$\Rightarrow 576=432 \times 1+144$

 

$\Rightarrow 432=144 \times 3+0$

Therefore the HCF of 432 and 144 is 144.

Hence the HCF of 10224 and 9648 is 144