Prime factorization of $$$1599$$$

Find the prime factorization of $$$1599$$$.

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

Determine whether $$$1599$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1599$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1599$$$ by $$${\color{green}3}$$$: $$$\frac{1599}{3} = {\color{red}533}$$$.

Determine whether $$$533$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$533$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$533$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$533$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$533$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$533$$$ by $$${\color{green}13}$$$: $$$\frac{533}{13} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$1599 = 3 \cdot 13 \cdot 41$$$.

The prime factorization is $$$1599 = 3 \cdot 13 \cdot 41$$$A.