Question

What is the prime factorization of $99$ ?

Answer 1

Hint: Prime Factorization is the process of finding the prime numbers, which are multiplied to get the original numbers. A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers. Examples of prime numbers are $2,3,5,7,11..$ . These numbers can’t be written as a product of any smaller natural numbers which are greater than $1$ . So let us break down $99$ and write as a product of smaller natural numbers which are greater than $1$ .

Complete step by step solution:
$99$ is divisible by $3$ . When we divide it by $3$ , we get $33$. So let us write it mathematically .
Upon doing so, we get the following :
$\Rightarrow 99=3\times 33$
$33$ is divisible by $3$ . When we divide it by $3$ , we get $11$. So let us write it mathematically .
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 99=3\times 33 \\
 & \Rightarrow 99=3\times 3\times 11 \\
\end{align}$
$11$ is a prime number. We can’t write it as a product of smaller natural numbers which are greater than $1$. So this can’t be expanded further.
Let us write $3\times 3$ as ${{3}^{2}}$.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 99=3\times 33 \\
 & \Rightarrow 99=3\times 3\times 11 \\
 & \Rightarrow 99={{3}^{2}}\times 11 \\
\end{align}$

$\therefore $ The prime factorization of $99$ is ${{3}^{2}}\times 11$

Note: We are not supposed to write ${{3}^{2}}$ as $9$ since $9$ is a composite number. It is not a prime number. Prime Factorization is the product of prime numbers. Composite numbers are those which can be written as a product of smaller natural numbers. Prime factorization is used to find the least common multiple of two numbers and it is also used in many other concepts. We should be careful while solving as it might lead to errors.