# Prime factorization of $804$

The calculator will find the prime factorization of $804$, with steps shown.

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Find the prime factorization of $804$.

### Solution

Start with the number $2$.

Determine whether $804$ is divisible by $2$.

It is divisible, thus, divide $804$ by ${\color{green}2}$: $\frac{804}{2} = {\color{red}402}$.

Determine whether $402$ is divisible by $2$.

It is divisible, thus, divide $402$ by ${\color{green}2}$: $\frac{402}{2} = {\color{red}201}$.

Determine whether $201$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $201$ is divisible by $3$.

It is divisible, thus, divide $201$ by ${\color{green}3}$: $\frac{201}{3} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $804 = 2^{2} \cdot 3 \cdot 67$.

The prime factorization is $804 = 2^{2} \cdot 3 \cdot 67$A.