Prime factorization of $$$664$$$

Find the prime factorization of $$$664$$$.

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

Determine whether $$$664$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$664$$$ by $$${\color{green}2}$$$: $$$\frac{664}{2} = {\color{red}332}$$$.

Determine whether $$$332$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$332$$$ by $$${\color{green}2}$$$: $$$\frac{332}{2} = {\color{red}166}$$$.

Determine whether $$$166$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$166$$$ by $$${\color{green}2}$$$: $$$\frac{166}{2} = {\color{red}83}$$$.

The prime number $$${\color{green}83}$$$ has no other factors then $$$1$$$ and $$${\color{green}83}$$$: $$$\frac{83}{83} = {\color{red}1}$$$.

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: $$$664 = 2^{3} \cdot 83$$$.

The prime factorization is $$$664 = 2^{3} \cdot 83$$$A.