Question

What is the prime factorization of $72$?

Answer 1

Determine the prime factorization of $72$.

Prime numbers are whole numbers greater than one that can only be divided equally by themselves and one.

Divide $72$ by only prime numbers to obtain the prime factorization.

The number $72$ is divided by $2$, which is a prime number.

$\begin{array}{rcl}72÷2& =& 36\\ & \Rightarrow & 36÷2=18\\ & \Rightarrow & 18÷2=9\end{array}$

The number $9$ is divided by $3$, which is a prime number.

$\begin{array}{rcl}9÷3& =& 3\\ & \Rightarrow & 3÷3=1\end{array}$

Thus, the prime factorization of $72$ is obtained as follows:

$\begin{array}{rcl}72& =& 2\times 2\times 2\times 3\times 3\\ & \Rightarrow & 64=2^3\times 3^2\end{array}$

Hence, the prime factorization of $72$ is $\begin{array}{rcl}& & 2^3\times 3^2\end{array}$.