# Prime factorization of $333$

The calculator will find the prime factorization of $333$, with steps shown.

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Find the prime factorization of $333$.

### Solution

Start with the number $2$.

Determine whether $333$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $333$ is divisible by $3$.

It is divisible, thus, divide $333$ by ${\color{green}3}$: $\frac{333}{3} = {\color{red}111}$.

Determine whether $111$ is divisible by $3$.

It is divisible, thus, divide $111$ by ${\color{green}3}$: $\frac{111}{3} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $333 = 3^{2} \cdot 37$.

The prime factorization is $333 = 3^{2} \cdot 37$A.