# Prime factorization of $204$

The calculator will find the prime factorization of $204$, with steps shown.

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Find the prime factorization of $204$.

### Solution

Start with the number $2$.

Determine whether $204$ is divisible by $2$.

It is divisible, thus, divide $204$ by ${\color{green}2}$: $\frac{204}{2} = {\color{red}102}$.

Determine whether $102$ is divisible by $2$.

It is divisible, thus, divide $102$ by ${\color{green}2}$: $\frac{102}{2} = {\color{red}51}$.

Determine whether $51$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $51$ is divisible by $3$.

It is divisible, thus, divide $51$ by ${\color{green}3}$: $\frac{51}{3} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $204 = 2^{2} \cdot 3 \cdot 17$.

The prime factorization is $204 = 2^{2} \cdot 3 \cdot 17$A.