Using Euclid's division algorithm, find the HCF of 250, 175 and 425.

Given :

The given numbers are 250, 175, and 425.

To find :

We have to find the HCF of 250, 175, and 425 by using Euclid's division algorithm.

Solution :

By Euclid's division algorithm,

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

Here, $425 > 250 > 175$

So, apply Euclid's division lemma for 425 and 250

$425 = 250 \times 1 + 175$

Remainder $=175$

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

Now, consider 250 as the dividend and 175 as the divisor,

$250 = 175 \times 1 + 75$

Remainder $=75$

Now, consider 175 as the dividend and 75 as the divisor,

$175 = 75 \times 2 + 25$

Remainder $=25$

Now, consider 75 as the dividend and 25 as the divisor,

$75 = 25 \times 3 + 0$

Remainder $=0$

So, HCF of 425 and 250 is 25.

Now, apply Euclid's division lemma for 175 and 25,

$175 = 25 \times 7 + 0$

Remainder $=0$

 Therefore, HCF of 425 , 250 and 175 is 25.