Question

use euclid's division algorithm to find the HCF of 900 and 270

Answer 1

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a=bq+r
a = 900
b= 270
q =quotient and r= remainder
so,when u divide 900 with 270 u will get
q= 3 and r= 90
sub values
900= 270(3)+90
270*3=810
900= 810+90
900=900
hcf= 3

Answer 2

$<b><i>$

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.