Question

Use Euclid's algorithm to find the HCF of
(1) 900 and 270
(ii) 196 and 38220
Use division ole​

Answer 1

SOLUTION

TO DETERMINE

Use Euclid's algorithm to find the HCF of

(1) 900 and 270

(ii) 196 and 38220

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

(i) Here two integers are 900 and 270

$900 = 3 \times 270 + 90$

$270 = 3 \times 90 + 0$

So 90 is the last non zero Remainder

Also

$90= 900 - (3 \times 270)$

Hence HCF of 900 and 270 is 90

(ii) Here two integers are 196 and 38220

38220 = ( 196 × 195 ) + 0

So Remainder = 0

So 38220 is completely divisible by 196

Hence HCF of 196 and 38220 is 196

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