The H.C.F of 867 and 255 using Euclid’s division algorithm is ____

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Detailed Solution

The H.C.F of 867 and 255 using Euclid’s division algorithm is 51.
Given two numbers are 867 and 255.
We have to find the H.C.F of both numbers using Euclid’s division algorithm.
According to Euclid’s division lemma, the relation of a and b is

a = b q + r

where a and b are positive integers, r = remainder and q = quotient.
Since 867>255, a = 867 and b = 255.

867 = 255 × 3 + 102

Since, the remainder is not 0,
a = 255 and b = 102.

255 = 102 × 2 + 51

Since, the remainder is not 0,
a = 102 and b = 51.
102 = 51 ×2 + 0
Now, the remainder is 0, so H.C.F. is 51.
H.C.F of 867 and 255 is 51.

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