Use Euclid’s division algorithm to find the HCF of 136, 170 and 255.

1.	Use Euclid’s division algorithm to find the HCF of 136, 170 and 255.
Answer» Let’s first choose 136 and 170 to find the HCF by using Euclid’s division lemma. Thus, we obtain 170 = 136 x 1 + 34 Since the remainder 34 ≠ 0. So we apply the division lemma to the divisor 136 and remainder 34. We get, 136 = 34 x 4 + 0 The remainder at this stage is 0, the divisor will be the HCF i.e., 34 for 136 and 170. Now, we again use Euclid’s division lemma to find the HCF of 34 and 255. And we get, 255 = 34 x 7 + 17 Since the remainder 17 ≠ 0. So we apply the division lemma to the divisor 34 and remainder 17. We get, 34 = 17 x 2 + 0 So, this stage has remainder 0. Thus, the HCF of the third number 255 and 34 is 17. Hence, the HCF of 136, 170 and 255 is 17.

Answer»

Let’s first choose 136 and 170 to find the HCF by using Euclid’s division lemma.

Thus, we obtain

170 = 136 x 1 + 34

Since the remainder 34 ≠ 0. So we apply the division lemma to the divisor 136 and remainder 34. We get,

136 = 34 x 4 + 0

The remainder at this stage is 0, the divisor will be the HCF i.e., 34 for 136 and 170.

Now, we again use Euclid’s division lemma to find the HCF of 34 and 255. And we get,

255 = 34 x 7 + 17

Since the remainder 17 ≠ 0. So we apply the division lemma to the divisor 34 and remainder 17. We get,

34 = 17 x 2 + 0

So, this stage has remainder 0. Thus, the HCF of the third number 255 and 34 is 17.

Hence, the HCF of 136, 170 and 255 is 17.

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