Question

1. Use Euclid’s division algorithm to find the HCF of :-
i. 135 and 225

Answer 1

Answer:

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1) 135 and 225

As you can see, from the question 225 is greater than 135. Therefore, by Euclid’s division algorithm, we have,

225 = 135 × 1 + 90

Now, remainder 90 ≠ 0, thus again using division lemma for 90, we get,

135 = 90 × 1 + 45

Again, 45 ≠ 0, repeating the above step for 45, we get,

90 = 45 × 2 + 0

The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45, therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45.

Hence, the HCF of 225 and 135 is 45.

Answer 2

Answer:

Given integers here are 225 and 135. On comparing, we find 225 > 135.

So, by applying Euclid’s division lemma to 225 and 135, we get

225 = 135 x 1 + 90

Since the remainder ≠ 0. So we apply the division lemma to the divisor 135 and remainder 90.

⇒ 135 = 90 x 1 + 45

Now we apply the division lemma to the new divisor 90 and remainder 45.

⇒ 90 = 45 x 2 + 0

Since the remainder at this stage is 0, the divisor will be the HCF.

Hence, the H.C.F of 225 and 135 is 45.

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