# Prime factorization of $3123$

The calculator will find the prime factorization of $3123$, with steps shown.

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Find the prime factorization of $3123$.

### Solution

Start with the number $2$.

Determine whether $3123$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3123$ is divisible by $3$.

It is divisible, thus, divide $3123$ by ${\color{green}3}$: $\frac{3123}{3} = {\color{red}1041}$.

Determine whether $1041$ is divisible by $3$.

It is divisible, thus, divide $1041$ by ${\color{green}3}$: $\frac{1041}{3} = {\color{red}347}$.

The prime number ${\color{green}347}$ has no other factors then $1$ and ${\color{green}347}$: $\frac{347}{347} = {\color{red}1}$.

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: $3123 = 3^{2} \cdot 347$.

The prime factorization is $3123 = 3^{2} \cdot 347$A.