The H.C.F of 135 and 225 using Euclid’s division algorithm is ____

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Detailed Solution

The H.C.F of 135 and 225 using Euclid’s division algorithm is 45.
Given two numbers 135 and 225.
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 225>135, a = 225 and b = 135.

225 = 135 × 1 + 90

Since, remainder is not 0,
a = 135 and b = 90.

135 = 90 × 1 + 45

Since, remainder is not 0,
a = 90 and b = 45.

90 = 45 × 2 + 0

Now, the remainder = 0.
So, H.C.F. = 45.
H.C. F of 135 and 225 is 45.

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