Question

What is the prime factorization of $180$?

Answer 1

Determine the prime factorization of $180$.

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

Divide $180$ by only prime numbers to obtain the prime factorization.

$$\begin{gathered} 180=2\times 90 \\ =2\times 2\times 45 \\ =2\times 2\times 5\times 9 \\ =2\times 2\times 5\times 3\times 3 \end{gathered}$$

$\begin{array}{rcl}\therefore 180& =& 2^2\times 3^2\times 5\end{array}$

Hence, the prime factorization of $180$ is $\begin{array}{l}{2}^2\times 3^2\times 5\end{array}$.