Use Euclid's division algorithm to find the HCF of:136, 170 and 255

Given: 136, 170 and 255.

To find: Here we have to find the HCF of the given numbers.

Solution:

First, let's find HCF of 136 and 170 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $170\ =\ 136\ \times\ 1\ +\ 34$

Now, consider the divisor 136 and the remainder 34, and apply the division lemma to get:
• $136\ =\ 34\ \times\ 4\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 136 and 170 is the divisor at this stage, i.e., 34.

Now, let's find HCF of 34 and 255 using Euclid's division algorithm:

Using Euclid’s lemma to get:
• $255\ =\ 34\ \times\ 7\ +\ 17$
Now, consider the divisor 34 and the remainder 17, and apply the division lemma to get:
• $34\ =\ 17\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 34 and 255 is the divisor at this stage, i.e., 17.

So, HCF of 136, 170 and 255 is 17.

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Updated on: 10-Oct-2022

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