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Find the HCF of 255 and 867 by Euclid's division algorithm.

Asked by Topperlearning User 11th December 2013, 10:05 AM
Answered by Expert
Answer:

Since 867 > 255, apply Euclid's division lemma, to a =867 and b=255 to find q and r such that 867 = 255q+r, 0 r < 255

On dividing 867 by 255 we get quotient as 3 and remainder as 102

i.e 867 = 255 3 + 102

Since remainder 102 0, we apply the division lemma to a=255 and b= 102 to find whole numbers q and r such that 255 = 102q + r where 0 r<102

On dividing 255 by 102 we get quotient as 2 and remainder as 51

i.e 255 = 102 x 2 + 51

Again remainder 51 is non zero, so we apply the division lemma to a=102 and b= 51 to find whole numbers q and r such that 102 = 51 q + r where 0 r<51 

On dividing 102 by 51 quotient is 2 and remainder is 0 i.e 102 = 51 x 2 + 0

Since the remainder is zero, the divisor at this stage is the HCF

Since the divisor at this stage is 51,therefore, HCF of 867 and 255 is 51.

Answered by Expert 11th December 2013, 12:05 PM
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