Prime factorization of $$$3204$$$

Find the prime factorization of $$$3204$$$.

Start with the number $$$2$$$.

Determine whether $$$3204$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3204$$$ by $$${\color{green}2}$$$: $$$\frac{3204}{2} = {\color{red}1602}$$$.

Determine whether $$$1602$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1602$$$ by $$${\color{green}2}$$$: $$$\frac{1602}{2} = {\color{red}801}$$$.

Determine whether $$$801$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$801$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$801$$$ by $$${\color{green}3}$$$: $$$\frac{801}{3} = {\color{red}267}$$$.

Determine whether $$$267$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$267$$$ by $$${\color{green}3}$$$: $$$\frac{267}{3} = {\color{red}89}$$$.

The prime number $$${\color{green}89}$$$ has no other factors then $$$1$$$ and $$${\color{green}89}$$$: $$$\frac{89}{89} = {\color{red}1}$$$.

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: $$$3204 = 2^{2} \cdot 3^{2} \cdot 89$$$.

The prime factorization is $$$3204 = 2^{2} \cdot 3^{2} \cdot 89$$$A.