# Prime factorization of $3081$

The calculator will find the prime factorization of $3081$, with steps shown.

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Find the prime factorization of $3081$.

### Solution

Start with the number $2$.

Determine whether $3081$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3081$ is divisible by $3$.

It is divisible, thus, divide $3081$ by ${\color{green}3}$: $\frac{3081}{3} = {\color{red}1027}$.

Determine whether $1027$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1027$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1027$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1027$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $1027$ is divisible by $13$.

It is divisible, thus, divide $1027$ by ${\color{green}13}$: $\frac{1027}{13} = {\color{red}79}$.

The prime number ${\color{green}79}$ has no other factors then $1$ and ${\color{green}79}$: $\frac{79}{79} = {\color{red}1}$.

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: $3081 = 3 \cdot 13 \cdot 79$.

The prime factorization is $3081 = 3 \cdot 13 \cdot 79$A.