Question

What is the prime factorization of 66?

Answer 1

Hint: Factors are those numbers which divide the given number completely and leave 0 remainder. In this question, we are finding the prime factors of 66, so we need to find the numbers that are prime and divide 66 completely and leave 0 remainder. As 66 is a composite number, it will have more than two factors.

Complete step by step solution:
In this question, we are supposed to find the prime factors of 66.
First of all, let us understand what prime factors are.
Prime factors are those numbers which are prime and when divided by the given number gives remainder as 0.
In our case, we have to find the prime factors of 66. So, the numbers that are prime and when divided by 66 leaves 0 remainder are known as the prime factors of 66. For example, if 3 is the factor of 66, then 66 divided by 3 must leave 0 remainder.
$66 \div 3 = 22$ - - - - - - - [0 remainder]
Hence, 3 is one of the factors of 66.
Now, as 66 is a composite number, it will have more than two factors.
Let us find all the factors of 66.
To find the factors of 66, we need to find the numbers which divide 66 and leave 0 remainder.
$
  66 \div 66 = 1 \\
  66 \div 33 = 2 \\
  66 \div 22 = 3 \\
  66 \div 11 = 6 \\
  66 \div 6 = 11 \\
  66 \div 3 = 22 \\
  66 \div 2 = 33 \\
  66 \div 1 = 66 \\
 $
Here, all these numbers when divided with 66 leaves 0 remainder.
So, the factors of 66$ = 1,2,3,6,11,22,33,66$.
Now, we need to find out prime factors out of these factors.
So, the prime factors of 66 are 2, 3 and 11.

Note:
Prime factorization is the method of expressing a number in terms of product of only prime numbers, whereas normal factorization can be expressed as a product of composite numbers too.
For example: $66 = 2 \times 33 = 2 \times 3 \times 11$