Prime factorization of $$$318$$$

Find the prime factorization of $$$318$$$.

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

Determine whether $$$318$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$318$$$ by $$${\color{green}2}$$$: $$$\frac{318}{2} = {\color{red}159}$$$.

Determine whether $$$159$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$159$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$159$$$ by $$${\color{green}3}$$$: $$$\frac{159}{3} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$318 = 2 \cdot 3 \cdot 53$$$.

The prime factorization is $$$318 = 2 \cdot 3 \cdot 53$$$A.