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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

135 and 225
As you can see, from the question 225 is greater than 135.
Therefore, byEuclid’s division algorithm, wehave,

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.

Thanks

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