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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 5964 Points
11 months 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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