Question: 1: Use Euclid’s division algorithm to find the HCF of:
I. 135 and 225
| Class | 10th |
| Subject | Maths |
| Chapter | Real Numbers |
| Exercise | 1.1 |
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Solution:
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.