Prime factorization of $$$312$$$

Find the prime factorization of $$$312$$$.

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

Determine whether $$$312$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$312$$$ by $$${\color{green}2}$$$: $$$\frac{312}{2} = {\color{red}156}$$$.

Determine whether $$$156$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$156$$$ by $$${\color{green}2}$$$: $$$\frac{156}{2} = {\color{red}78}$$$.

Determine whether $$$78$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$78$$$ by $$${\color{green}2}$$$: $$$\frac{78}{2} = {\color{red}39}$$$.

Determine whether $$$39$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$39$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$39$$$ by $$${\color{green}3}$$$: $$$\frac{39}{3} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$312 = 2^{3} \cdot 3 \cdot 13$$$.

The prime factorization is $$$312 = 2^{3} \cdot 3 \cdot 13$$$A.