# Prime factorization of $3141$

The calculator will find the prime factorization of $3141$, with steps shown.

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Find the prime factorization of $3141$.

### Solution

Start with the number $2$.

Determine whether $3141$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3141$ is divisible by $3$.

It is divisible, thus, divide $3141$ by ${\color{green}3}$: $\frac{3141}{3} = {\color{red}1047}$.

Determine whether $1047$ is divisible by $3$.

It is divisible, thus, divide $1047$ by ${\color{green}3}$: $\frac{1047}{3} = {\color{red}349}$.

The prime number ${\color{green}349}$ has no other factors then $1$ and ${\color{green}349}$: $\frac{349}{349} = {\color{red}1}$.

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: $3141 = 3^{2} \cdot 349$.

The prime factorization is $3141 = 3^{2} \cdot 349$A.