Prime factorization of $$$1125$$$

Find the prime factorization of $$$1125$$$.

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.