Prime factorization of $$$18$$$

Find the prime factorization of $$$18$$$.

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

Determine whether $$$18$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$18$$$ by $$${\color{green}2}$$$: $$$\frac{18}{2} = {\color{red}9}$$$.

Determine whether $$$9$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$9$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$9$$$ by $$${\color{green}3}$$$: $$$\frac{9}{3} = {\color{red}3}$$$.

The prime number $$${\color{green}3}$$$ has no other factors then $$$1$$$ and $$${\color{green}3}$$$: $$$\frac{3}{3} = {\color{red}1}$$$.

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: $$$18 = 2 \cdot 3^{2}$$$.

The prime factorization is $$$18 = 2 \cdot 3^{2}$$$A.