# Prime factorization of $2504$

The calculator will find the prime factorization of $2504$, with steps shown.

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Find the prime factorization of $2504$.

### Solution

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.