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Is the statement true?

The pair of numbers 231,396 are co-prime numbers using Euclid division lemma algorithm.

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True

False

answer is B.

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Detailed Solution

Given,
The numbers 231,396 are co-prime numbers.
As we know,
The Euclid division lemma on any variable

a

and

b

is,

⇒ a = b q + r

, where

0 ≤ r ≤ b

for some whole

q

and

r

.
Let

a = 231, b = 396

.
By using Euclid division algorithm in numbers (231,396) we have,

\Rightarrow 396 = 231 \times 1 + 165

We continue the process till the last non-zero remainder is HCF of

a

and

b

\Rightarrow 231 = 165 \times 1 + 66

\Rightarrow 165 = 66 \times 2 + 33

\Rightarrow 66 = 33 \times 2 + 0

Thus, the last non-zero remainder is 33.
Hence, HCF of (231,396) = 33.
So, the given statement is false.
Thus, the correct statement is that the numbers 231 and 396 are not co-prime.
Therefore, option (2) is the correct answer.

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