Prime factorization of $$$3312$$$

Find the prime factorization of $$$3312$$$.

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

Determine whether $$$3312$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3312$$$ by $$${\color{green}2}$$$: $$$\frac{3312}{2} = {\color{red}1656}$$$.

Determine whether $$$1656$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1656$$$ by $$${\color{green}2}$$$: $$$\frac{1656}{2} = {\color{red}828}$$$.

Determine whether $$$828$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$828$$$ by $$${\color{green}2}$$$: $$$\frac{828}{2} = {\color{red}414}$$$.

Determine whether $$$414$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$414$$$ by $$${\color{green}2}$$$: $$$\frac{414}{2} = {\color{red}207}$$$.

Determine whether $$$207$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$207$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$207$$$ by $$${\color{green}3}$$$: $$$\frac{207}{3} = {\color{red}69}$$$.

Determine whether $$$69$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$69$$$ by $$${\color{green}3}$$$: $$$\frac{69}{3} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$3312 = 2^{4} \cdot 3^{2} \cdot 23$$$.

The prime factorization is $$$3312 = 2^{4} \cdot 3^{2} \cdot 23$$$A.