Prime factorization of $$$2613$$$

Find the prime factorization of $$$2613$$$.

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.