# Prime factorization of $75$

The calculator will find the prime factorization of $75$, with steps shown.

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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.