Prime factorization of $$$4015$$$

Find the prime factorization of $$$4015$$$.

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

Determine whether $$$4015$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4015$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$4015$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$4015$$$ by $$${\color{green}5}$$$: $$$\frac{4015}{5} = {\color{red}803}$$$.

Determine whether $$$803$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$803$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$803$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$803$$$ by $$${\color{green}11}$$$: $$$\frac{803}{11} = {\color{red}73}$$$.

The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.

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: $$$4015 = 5 \cdot 11 \cdot 73$$$.

The prime factorization is $$$4015 = 5 \cdot 11 \cdot 73$$$A.