# Prime factorization of $522$

The calculator will find the prime factorization of $522$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $522$.

### Solution

Start with the number $2$.

Determine whether $522$ is divisible by $2$.

It is divisible, thus, divide $522$ by ${\color{green}2}$: $\frac{522}{2} = {\color{red}261}$.

Determine whether $261$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $261$ is divisible by $3$.

It is divisible, thus, divide $261$ by ${\color{green}3}$: $\frac{261}{3} = {\color{red}87}$.

Determine whether $87$ is divisible by $3$.

It is divisible, thus, divide $87$ by ${\color{green}3}$: $\frac{87}{3} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $522 = 2 \cdot 3^{2} \cdot 29$.

The prime factorization is $522 = 2 \cdot 3^{2} \cdot 29$A.