Question

Why isn’t $57$ a prime number?

Answer 1

Hint: A prime number is defined as the one which does not have factors other than one and the number itself. Therefore, in order to check the given number to be a prime number or not, we need to obtain its factors. For this, we can try out the test for the divisibility by the different numbers.

Complete step-by-step solution:
The number given in the above question is equal to $57$. We know that a prime number is that which has no factor other than one and the number itself. Therefore, for testing it to be a prime number or not, we have to try figuring out its factors. For this, we apply the test for the divisibility by different numbers.
Let us first apply the test for divisibility by two. We know that a number is divisible by two if it is even. The given number $57$ is however odd. Therefore, the given number is not divisible by two. Thus, two is not the factor of $57$.
Now, let us apply the test for divisibility by three. We know that a number is divisible by three if the sum of its digits is divisible by three. In the given number $57$ the digits are $5$ and $7$, the sum of which is equal to $12$, which is divisible by three. So the given number $57$ is divisible by three. Therefore, three is the factor of the given number.
Now, since we got the factor of three for $57$, which is not one and the number $57$, the number is not a prime number.
Hence, we finally proved that $57$ is not a prime number.

Note: For solving these types of questions, we must remember the different tests for the divisibility of the different numbers. We must not think of the odd numbers as the prime numbers. An odd number may or may not be a prime number.