Question

Use euclid division algorithm to find the hcf of 900 and 270

Answer 1

Using Euclid's division algorithm,

divide the larger number by smaller number
900 ÷ 270 = 3, and 90 remainder

divide the divisor by remiander
270 ÷ 90 = 3, and remainder is 0

So HCF is 90.

Answer 2

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Euclid’s Division is a method for finding the HCF (highest common factor) of two given integers. According to Euclid’s Division Algorithm, For any two positive integers, ‘a’ and ‘b’, there exists a unique pair of integers ‘q’ and ‘r’ which satisfy the relation:

a = bq + r , 0 ≤ r ≤ b

Given integers 900 and 270. Clearly 900>270.

By applying division lemma

⇒ 900 = 270×3 + 90

Since remainder 0, applying division lemma on 270 and 90

⇒ 270 = 90×3 + 0

∵ remainder = 0,

∴ the HCF of 900 and 270 is 90.