Prime factorization of $$$656$$$

Find the prime factorization of $$$656$$$.

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

Determine whether $$$656$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$656$$$ by $$${\color{green}2}$$$: $$$\frac{656}{2} = {\color{red}328}$$$.

Determine whether $$$328$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$328$$$ by $$${\color{green}2}$$$: $$$\frac{328}{2} = {\color{red}164}$$$.

Determine whether $$$164$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$164$$$ by $$${\color{green}2}$$$: $$$\frac{164}{2} = {\color{red}82}$$$.

Determine whether $$$82$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$82$$$ by $$${\color{green}2}$$$: $$$\frac{82}{2} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$656 = 2^{4} \cdot 41$$$.

The prime factorization is $$$656 = 2^{4} \cdot 41$$$A.