Prime factorization of $$$3616$$$

Find the prime factorization of $$$3616$$$.

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

Determine whether $$$3616$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3616$$$ by $$${\color{green}2}$$$: $$$\frac{3616}{2} = {\color{red}1808}$$$.

Determine whether $$$1808$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1808$$$ by $$${\color{green}2}$$$: $$$\frac{1808}{2} = {\color{red}904}$$$.

Determine whether $$$904$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$904$$$ by $$${\color{green}2}$$$: $$$\frac{904}{2} = {\color{red}452}$$$.

Determine whether $$$452$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$452$$$ by $$${\color{green}2}$$$: $$$\frac{452}{2} = {\color{red}226}$$$.

Determine whether $$$226$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$226$$$ by $$${\color{green}2}$$$: $$$\frac{226}{2} = {\color{red}113}$$$.

The prime number $$${\color{green}113}$$$ has no other factors then $$$1$$$ and $$${\color{green}113}$$$: $$$\frac{113}{113} = {\color{red}1}$$$.

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: $$$3616 = 2^{5} \cdot 113$$$.

The prime factorization is $$$3616 = 2^{5} \cdot 113$$$A.