Using Euclid's division algorithm find the HCF of 455 and 255.

Given :

The given numbers are 455 and 255.

To find :

We have to the HCF of the given numbers 455 and 255 by using Euclid's division algorithm.

Solution :

By Euclid's division lemma,

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

Here, $455 > 255$

So, divide 455 by 255,

$455 = 255 \times 1 + 200$

Remainder $= 200$

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

Now, consider 255 as the dividend and 200 as the divisor,

$255 = 200 \times 1 + 55$

Remainder $= 55$

Now, consider 200 as the dividend and 55 as the divisor,

 $200 = 55 \times 3 + 35$

Remainder $=35$

Now, consider 55 as the dividend and 35 as the divisor,

 $55 = 35 \times 1 + 20$

Remainder $=20$

Now, consider 35 as the dividend and 20 as the divisor,

 $35 = 20 \times 1 + 15$

Remainder $=15$

Now, consider 20 as the dividend and 15 as the divisor,

 $20 = 15 \times 1 + 5$

Remainder $=5$

Now, consider 15 as the dividend and 5 as the divisor,

 $15 = 5 \times 3 + 0$

Remainder $=0$

Therefore, HCF of 455 and 255 is 5.

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Updated on: 10-Oct-2022

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