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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.