Prime factorization of $$$3336$$$

Find the prime factorization of $$$3336$$$.

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

Determine whether $$$3336$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3336$$$ by $$${\color{green}2}$$$: $$$\frac{3336}{2} = {\color{red}1668}$$$.

Determine whether $$$1668$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1668$$$ by $$${\color{green}2}$$$: $$$\frac{1668}{2} = {\color{red}834}$$$.

Determine whether $$$834$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$834$$$ by $$${\color{green}2}$$$: $$$\frac{834}{2} = {\color{red}417}$$$.

Determine whether $$$417$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$417$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$417$$$ by $$${\color{green}3}$$$: $$$\frac{417}{3} = {\color{red}139}$$$.

The prime number $$${\color{green}139}$$$ has no other factors then $$$1$$$ and $$${\color{green}139}$$$: $$$\frac{139}{139} = {\color{red}1}$$$.

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: $$$3336 = 2^{3} \cdot 3 \cdot 139$$$.

The prime factorization is $$$3336 = 2^{3} \cdot 3 \cdot 139$$$A.