# Prime factorization of $3204$

The calculator will find the prime factorization of $3204$, with steps shown.

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Find the prime factorization of $3204$.

### Solution

Start with the number $2$.

Determine whether $3204$ is divisible by $2$.

It is divisible, thus, divide $3204$ by ${\color{green}2}$: $\frac{3204}{2} = {\color{red}1602}$.

Determine whether $1602$ is divisible by $2$.

It is divisible, thus, divide $1602$ by ${\color{green}2}$: $\frac{1602}{2} = {\color{red}801}$.

Determine whether $801$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $801$ is divisible by $3$.

It is divisible, thus, divide $801$ by ${\color{green}3}$: $\frac{801}{3} = {\color{red}267}$.

Determine whether $267$ is divisible by $3$.

It is divisible, thus, divide $267$ by ${\color{green}3}$: $\frac{267}{3} = {\color{red}89}$.

The prime number ${\color{green}89}$ has no other factors then $1$ and ${\color{green}89}$: $\frac{89}{89} = {\color{red}1}$.

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: $3204 = 2^{2} \cdot 3^{2} \cdot 89$.

The prime factorization is $3204 = 2^{2} \cdot 3^{2} \cdot 89$A.