Prime factorization of $$$2504$$$

Find the prime factorization of $$$2504$$$.

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

Determine whether $$$2504$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2504$$$ by $$${\color{green}2}$$$: $$$\frac{2504}{2} = {\color{red}1252}$$$.

Determine whether $$$1252$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1252$$$ by $$${\color{green}2}$$$: $$$\frac{1252}{2} = {\color{red}626}$$$.

Determine whether $$$626$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$626$$$ by $$${\color{green}2}$$$: $$$\frac{626}{2} = {\color{red}313}$$$.

The prime number $$${\color{green}313}$$$ has no other factors then $$$1$$$ and $$${\color{green}313}$$$: $$$\frac{313}{313} = {\color{red}1}$$$.

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: $$$2504 = 2^{3} \cdot 313$$$.

The prime factorization is $$$2504 = 2^{3} \cdot 313$$$A.