# Prime factorization of $1125$

The calculator will find the prime factorization of $1125$, with steps shown.

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Find the prime factorization of $1125$.

### Solution

Start with the number $2$.

Determine whether $1125$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1125$ is divisible by $3$.

It is divisible, thus, divide $1125$ by ${\color{green}3}$: $\frac{1125}{3} = {\color{red}375}$.

Determine whether $375$ is divisible by $3$.

It is divisible, thus, divide $375$ by ${\color{green}3}$: $\frac{375}{3} = {\color{red}125}$.

Determine whether $125$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $125$ is divisible by $5$.

It is divisible, thus, divide $125$ by ${\color{green}5}$: $\frac{125}{5} = {\color{red}25}$.

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: $1125 = 3^{2} \cdot 5^{3}$.

The prime factorization is $1125 = 3^{2} \cdot 5^{3}$A.