Question

The given pair of numbers 231,396 are ________.

A.Multiple of each other.

B.Factors of each other

C.Co-prime of each other

D.Having HCF as 33.

Answer 1

Hint: We will calculate H.C.F of the given numbers. We can calculate H.C.F using Euclid’s Algorithm which states that if there are two numbers $a$and $b$, then there exists $q$ and $r$ such that, $a = bq + r$, where$0 \leqslant r < b$. Continue the process till the remainder is 0. The divisor in that stage is the H.C.F of the two numbers.

Complete step-by-step answer:
When we want to find whether the two numbers are multiple factors or co-prime, we need to find the Highest common factor(HCF) of the two numbers.
We use Euclid’s Algorithm to find the Highest common factor of two positive integers.
According to algorithm, if  $ a $ and  $ b $  are two numbers such that,  $ a \geqslant b $ , then  $ a = bq + r $ , where $ 0 \leqslant r < b $
We have to apply Euclid’s Algorithm till the remainder is 0.
Taking  $ a = 396 $  and  $ b = 231 $ , we get,
 $ 396 = 231 \times 1 + 165 $
Now, take  $ a = 231 $  and  $ b = 165 $ , we get,
 $ 231 = 165 \times 1 + 66 $
Similarly, repeat the process until the remainder gets zero. The HCF will be the divisor in the last step.
 $ 165 = 66 \times 2 + 33 $
 $ 66 = 33 \times 2 + 0 $
Now, the remainder is 0. Hence, it is the last step in Euclid’s Algorithm.
The divisor in the last step is 33.
Therefore, 33 is the H.C.F of 396 and 231.
If we get HCF as 1 then numbers are co-prime.
Two different numbers can’t be multiple of each other and two different numbers can’t be factors of each other. So option A and B are not correct.
Hence, option D is the correct answer.

Note: If the given numbers have only 1 as the common factor, then the numbers are co-prime to each other. A multiple is a number that can be divided completely by another number. A factor is a number that divides a given number completely.