# Prime factorization of $2613$

The calculator will find the prime factorization of $2613$, with steps shown.

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Find the prime factorization of $2613$.

### Solution

Start with the number $2$.

Determine whether $2613$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2613$ is divisible by $3$.

It is divisible, thus, divide $2613$ by ${\color{green}3}$: $\frac{2613}{3} = {\color{red}871}$.

Determine whether $871$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $871$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $871$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $871$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $871$ is divisible by $13$.

It is divisible, thus, divide $871$ by ${\color{green}13}$: $\frac{871}{13} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $2613 = 3 \cdot 13 \cdot 67$.

The prime factorization is $2613 = 3 \cdot 13 \cdot 67$A.