Prime factorization of $$$1688$$$

Find the prime factorization of $$$1688$$$.

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

Determine whether $$$1688$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1688$$$ by $$${\color{green}2}$$$: $$$\frac{1688}{2} = {\color{red}844}$$$.

Determine whether $$$844$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$844$$$ by $$${\color{green}2}$$$: $$$\frac{844}{2} = {\color{red}422}$$$.

Determine whether $$$422$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$422$$$ by $$${\color{green}2}$$$: $$$\frac{422}{2} = {\color{red}211}$$$.

The prime number $$${\color{green}211}$$$ has no other factors then $$$1$$$ and $$${\color{green}211}$$$: $$$\frac{211}{211} = {\color{red}1}$$$.

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: $$$1688 = 2^{3} \cdot 211$$$.

The prime factorization is $$$1688 = 2^{3} \cdot 211$$$A.