Prime factorization of $$$688$$$

Find the prime factorization of $$$688$$$.

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

Determine whether $$$688$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$688$$$ by $$${\color{green}2}$$$: $$$\frac{688}{2} = {\color{red}344}$$$.

Determine whether $$$344$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$344$$$ by $$${\color{green}2}$$$: $$$\frac{344}{2} = {\color{red}172}$$$.

Determine whether $$$172$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$172$$$ by $$${\color{green}2}$$$: $$$\frac{172}{2} = {\color{red}86}$$$.

Determine whether $$$86$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$86$$$ by $$${\color{green}2}$$$: $$$\frac{86}{2} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$688 = 2^{4} \cdot 43$$$.

The prime factorization is $$$688 = 2^{4} \cdot 43$$$A.