# Prime factorization of $2004$

The calculator will find the prime factorization of $2004$, with steps shown.

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Find the prime factorization of $2004$.

### Solution

Start with the number $2$.

Determine whether $2004$ is divisible by $2$.

It is divisible, thus, divide $2004$ by ${\color{green}2}$: $\frac{2004}{2} = {\color{red}1002}$.

Determine whether $1002$ is divisible by $2$.

It is divisible, thus, divide $1002$ by ${\color{green}2}$: $\frac{1002}{2} = {\color{red}501}$.

Determine whether $501$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $501$ is divisible by $3$.

It is divisible, thus, divide $501$ by ${\color{green}3}$: $\frac{501}{3} = {\color{red}167}$.

The prime number ${\color{green}167}$ has no other factors then $1$ and ${\color{green}167}$: $\frac{167}{167} = {\color{red}1}$.

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: $2004 = 2^{2} \cdot 3 \cdot 167$.

The prime factorization is $2004 = 2^{2} \cdot 3 \cdot 167$A.