Question

by using Euclid's division algorithm to find HCF of 135 and 225

Answer 1

Hello dear friend..
Here, is Ur answer ....
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Sol.

Here 225 > 135
we apply the division lemma to 225 and 135, we get ,

$= > 225 = 135 \times 1 + 90 \\ = > 135 = 90 \times 1 = 45 \\ = > 90 = 45 \times 2 = 0$
The remainder has now become 0, so our procedure stops.
Since , The Divisor at this is 45.
The HCF of 135 and 225 is 45

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Answer 2

As you can see, from 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.