Prime factorization of $$$4016$$$

Find the prime factorization of $$$4016$$$.

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

Determine whether $$$4016$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4016$$$ by $$${\color{green}2}$$$: $$$\frac{4016}{2} = {\color{red}2008}$$$.

Determine whether $$$2008$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2008$$$ by $$${\color{green}2}$$$: $$$\frac{2008}{2} = {\color{red}1004}$$$.

Determine whether $$$1004$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1004$$$ by $$${\color{green}2}$$$: $$$\frac{1004}{2} = {\color{red}502}$$$.

Determine whether $$$502$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$502$$$ by $$${\color{green}2}$$$: $$$\frac{502}{2} = {\color{red}251}$$$.

The prime number $$${\color{green}251}$$$ has no other factors then $$$1$$$ and $$${\color{green}251}$$$: $$$\frac{251}{251} = {\color{red}1}$$$.

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: $$$4016 = 2^{4} \cdot 251$$$.

The prime factorization is $$$4016 = 2^{4} \cdot 251$$$A.