Question

Use Euclid's division algorithm to find the hcf of 900 and 270

Answer 1

900 =  270*3+9                                         270)900(3
                                                                        -810
 270=      9*30+0                                                =  9)270(30
                                                                                270
                                                                               =00

therefore 9 is the HCF

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.