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The HCF of $135$ and $225$ using Euclid's algorithm is

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41

42

43

45

answer is D.

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Detailed Solution

Given numbers are 135 and 225.
We need to find the H.C.F of the given numbers using Euclid’s algorithm.
According to the definition of Euclid's algorithm,

a = b \times q + r

where

0 \leq r < b .

Here, larger number

a

is dividend, smaller number

b

is divisor,

q

is a quotient and

r

is the remainder.

225 = 135 \times 1 + 90

[by Euclid’s algorithm]
Here,

a = 225

b = 135

q = 1

and

r = 90

135 = 90 \times 1 + 45

Here,

a = 135

b = 90

q = 1

and

r = 45

90 = 45 \times 2 + 0

Here,

a = 90

b = 45

q = 2

and

r = 0

.
Since the remainder is zero, therefore, last divisor

45

is the HCF of

135

and

225

∴

HCF of

135

and

225

45

.
Hence, option 4 is correct.

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