Question

Use Euclid's division algorithm to find the HCF of
(i) 184, 230 and 276 (ii) 136, 170 and 255​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

(I)

Let’s first choose 184 and 230 to find the HCF by using Euclid’s division lemma.

Thus, we obtain

230 = 184 x 1 + 46

Since the remainder 46 ≠ 0. So we apply the division lemma to the divisor 184 and remainder 46. We get,

184 = 46 x 4 + 0

The remainder at this stage is 0, the divisor will be the HCF i.e., 46 for 184 and 230.

Now, we again use Euclid’s division lemma to find the HCF of 46 and 276. And we get,

276 = 46 x 6 + 0

So, this stage has remainder 0. Thus, the HCF of the third number 276 and 46 is 46.

Hence, the HCF of 184, 230 and 276 is 46.

(ii)

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.