Find the HCF of 72, 120, 192 by Euclid's division method.

Given :

The given numbers are 72, 120, and 192.

To find :

We have to find the HCF of 72, 120, and 192 by using Euclid's division algorithm.

Solution :

By Euclid's division algorithm,

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

Here, $192 > 120 > 72$

So, apply Euclid's division lemma for 192 and 120

$192 = 120 \times 1 + 72$

Remainder $=72$

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

Now, consider 120 as the dividend and 72 as the divisor,

$120 = 72 \times 1 + 48 $

Remainder $=48$

Now, consider 72 as the dividend and 48 as the divisor,

$72 = 48 \times 1 + 24$

Remainder $=24$

Now, consider 48 as the dividend and 24 as the divisor,

$48 = 24 \times 2 + 0$

Remainder $=0$

So, HCF of 192 and 120 is 24.

Now, apply Euclid's division lemma for 72 and 24,

$72 = 24 \times 3 + 0$

Remainder $=0$

 Therefore, HCF of 192, 120, and 72 is 24.

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Updated on: 10-Oct-2022

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