Question

1. Find the HCF of 900 and 250 by using Euclid's division Algorithm?​

Answer 1

Answer:

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Answer 2

SOLUTION

TO DETERMINE

The HCF of 900 and 250 by using Euclid's division Algorithm

EVALUATION

Euclidean algorithm is an efficient method of finding the highest common factor of two given integers.

The method involves repeated application of the division algorithm

900 = ( 3 × 250 ) + 150

250 = ( 1 × 150 ) + 100

150 = ( 1 × 100 ) + 50

100 = ( 2 × 50 ) + 0

Thus we get

50

= 150 - ( 2 × 50 )

= 150 - 2 × ( 150 - 100 )

= 2 × 100 - 150

= 2 × ( 250 - 150 ) - 150

= 2 × 250 - 3 × 150

= 2 × 250 - 3 × [ 900 - ( 3 × 250 ) ]

= 11 × 250 - 3 × 900

∴ 11 × 250 - 3 × 900 = 50

Hence the required HCF = 50

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