Question

What is the prime factorization of $2025$?

Answer 1

Determine the prime factorization of $2025$.

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

Divide $2025$ by only prime numbers to obtain the prime factorization.

The number $2025$ is divided by $3$, which is a prime number.

$\begin{array}{rcl}2025÷3& =& 675\\ & \Rightarrow & 675÷3=225\\ & \Rightarrow & 225÷3=75\\ & \Rightarrow & 75÷3=25\end{array}$

Now, $25$ is divided by $5$, which is a prime number.

$\begin{array}{rcl}25÷5& =& 5\\ & \Rightarrow & 5÷5=1\end{array}$

Thus, the prime factorization of $2025$ is obtained as follows:

$\begin{array}{rcl}2025& =& 3\times 3\times 3\times 3\times 5\times 5\\ \therefore 2025& =& 3^4\times 5^2\end{array}$

Hence, the prime factorization of $2025$ is $\begin{array}{rcl}& & 3^4\times 5^2\end{array}$.