Prime factorization of $$$2915$$$

Find the prime factorization of $$$2915$$$.

Start with the number $$$2$$$.

Determine whether $$$2915$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$2915$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$2915$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$2915$$$ by $$${\color{green}5}$$$: $$$\frac{2915}{5} = {\color{red}583}$$$.

Determine whether $$$583$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$583$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$583$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$583$$$ by $$${\color{green}11}$$$: $$$\frac{583}{11} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$2915 = 5 \cdot 11 \cdot 53$$$.

The prime factorization is $$$2915 = 5 \cdot 11 \cdot 53$$$A.