# Prime Factorization Calculator

## Find prime factorization step by step

This calculator will find the prime factorization of the given number, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $75$.

### Solution

Start with the number $2$.

Determine whether $75$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $75$ is divisible by $3$.

It is divisible, thus, divide $75$ by ${\color{green}3}$: $\frac{75}{3} = {\color{red}25}$.

Determine whether $25$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $25$ is divisible by $5$.

It is divisible, thus, divide $25$ by ${\color{green}5}$: $\frac{25}{5} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

Since we have obtained $1$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $75 = 3 \cdot 5^{2}$.

The prime factorization is $75 = 3 \cdot 5^{2}$A.