# Prime factorization of $3114$

The calculator will find the prime factorization of $3114$, with steps shown.

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Find the prime factorization of $3114$.

### Solution

Start with the number $2$.

Determine whether $3114$ is divisible by $2$.

It is divisible, thus, divide $3114$ by ${\color{green}2}$: $\frac{3114}{2} = {\color{red}1557}$.

Determine whether $1557$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1557$ is divisible by $3$.

It is divisible, thus, divide $1557$ by ${\color{green}3}$: $\frac{1557}{3} = {\color{red}519}$.

Determine whether $519$ is divisible by $3$.

It is divisible, thus, divide $519$ by ${\color{green}3}$: $\frac{519}{3} = {\color{red}173}$.

The prime number ${\color{green}173}$ has no other factors then $1$ and ${\color{green}173}$: $\frac{173}{173} = {\color{red}1}$.

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: $3114 = 2 \cdot 3^{2} \cdot 173$.

The prime factorization is $3114 = 2 \cdot 3^{2} \cdot 173$A.