# Prime factorization of $558$

The calculator will find the prime factorization of $558$, with steps shown.

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Find the prime factorization of $558$.

### Solution

Start with the number $2$.

Determine whether $558$ is divisible by $2$.

It is divisible, thus, divide $558$ by ${\color{green}2}$: $\frac{558}{2} = {\color{red}279}$.

Determine whether $279$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $279$ is divisible by $3$.

It is divisible, thus, divide $279$ by ${\color{green}3}$: $\frac{279}{3} = {\color{red}93}$.

Determine whether $93$ is divisible by $3$.

It is divisible, thus, divide $93$ by ${\color{green}3}$: $\frac{93}{3} = {\color{red}31}$.

The prime number ${\color{green}31}$ has no other factors then $1$ and ${\color{green}31}$: $\frac{31}{31} = {\color{red}1}$.

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: $558 = 2 \cdot 3^{2} \cdot 31$.

The prime factorization is $558 = 2 \cdot 3^{2} \cdot 31$A.