Prime factorization of $$$12$$$

Find the prime factorization of $$$12$$$.

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

Determine whether $$$12$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$12$$$ by $$${\color{green}2}$$$: $$$\frac{12}{2} = {\color{red}6}$$$.

Determine whether $$$6$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$6$$$ by $$${\color{green}2}$$$: $$$\frac{6}{2} = {\color{red}3}$$$.

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: $$$12 = 2^{2} \cdot 3$$$.

The prime factorization is $$$12 = 2^{2} \cdot 3$$$A.