# Prime factorization of $3138$

The calculator will find the prime factorization of $3138$, with steps shown.

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Find the prime factorization of $3138$.

### Solution

Start with the number $2$.

Determine whether $3138$ is divisible by $2$.

It is divisible, thus, divide $3138$ by ${\color{green}2}$: $\frac{3138}{2} = {\color{red}1569}$.

Determine whether $1569$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1569$ is divisible by $3$.

It is divisible, thus, divide $1569$ by ${\color{green}3}$: $\frac{1569}{3} = {\color{red}523}$.

The prime number ${\color{green}523}$ has no other factors then $1$ and ${\color{green}523}$: $\frac{523}{523} = {\color{red}1}$.

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: $3138 = 2 \cdot 3 \cdot 523$.

The prime factorization is $3138 = 2 \cdot 3 \cdot 523$A.