Question

What are the prime factors of 57?

Answer 1

Hint: To find the prime factors of 57, we are going to factorize this 57 which is done by dividing this number by 3, then whatsoever the quotient will remain, we will see by which number that number will get divisible. In this way, we will divide till we get the quotient as 1. Hence, the different numbers which we have divided are the prime factors of 57.

Complete step by step answer:
In the above problem, we are asked to find the prime factors of 57. For that, we are going to divide 57 by a number in such a way so that 57 will get completely divided. As the last number of 57 is not an even number so 57 won’t get divided by 2 and the sum of two numbers (5 and 7) is 12 and 12 is divisible by 3 so 57 will get divided by 3.
Dividing 57 by 3 we get,
$\begin{matrix}
   3 \\
   {} \\
\end{matrix}\left| \!{\overline {\,
 \begin{align}
  & 57 \\
 & 19 \\
\end{align} \,}} \right. $
From the above division, you can see that when we divide 57 by 3 we get 19.
Now, as 19 is a prime number so only 19 will be divisible by 19. So, dividing 19 by 19 we get,
$\begin{matrix}
   3 \\
   19 \\
   1 \\
\end{matrix}\left| \!{\overline {\,
 \begin{align}
  & 57 \\
 & 19 \\
 & 1 \\
\end{align} \,}} \right. $
In the above prime factorization, you can see that when dividing 19 by 19 we have got the quotient as 1 and when we get the quotient as 1 then we will stop the division.
From the above, the prime factors of 57 are equal to:
$3\times 19\times 1$

Hence, the prime factors of 57 are 3 and 19.

Note: The mistake that could be possible in the above problem is that you might write 1 as the prime factor which is wrong because 1 is not a prime number. You can say, 1 is a factor of 57 but not a prime factor so make sure, you won’t make this mistake.