Prime factorization of $$$3688$$$

Find the prime factorization of $$$3688$$$.

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

Determine whether $$$3688$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3688$$$ by $$${\color{green}2}$$$: $$$\frac{3688}{2} = {\color{red}1844}$$$.

Determine whether $$$1844$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1844$$$ by $$${\color{green}2}$$$: $$$\frac{1844}{2} = {\color{red}922}$$$.

Determine whether $$$922$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$922$$$ by $$${\color{green}2}$$$: $$$\frac{922}{2} = {\color{red}461}$$$.

The prime number $$${\color{green}461}$$$ has no other factors then $$$1$$$ and $$${\color{green}461}$$$: $$$\frac{461}{461} = {\color{red}1}$$$.

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: $$$3688 = 2^{3} \cdot 461$$$.

The prime factorization is $$$3688 = 2^{3} \cdot 461$$$A.