Using Euclid's division algorithm, find the HCF of 455 and 42.

Given :

The given numbers are 455 and 42.

To find :

We have to the HCF of the given numbers 455 and 42 by using Euclid's division algorithm.

Solution :

By Euclid's division lemma,

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

Here, $455 > 42$

So, divide 455 by 42,

$455 = 42 \times 10 + 35$

Remainder $= 35$

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

Now, consider 42 as the dividend and 35 as the divisor,

$42 = 35 \times 1 + 7$

Remainder $= 7$

Now, consider 35 as the dividend and 7 as the divisor,

 $35 = 7 \times 5 + 0$

Remainder $=0$

Therefore, HCF of 455 and 42 is 7.

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Updated on: 10-Oct-2022

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