Prime factorization of $$$3999$$$
Your Input
Find the prime factorization of $$$3999$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3999$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3999$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$3999$$$ by $$${\color{green}3}$$$: $$$\frac{3999}{3} = {\color{red}1333}$$$.
Determine whether $$$1333$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1333$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1333$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1333$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$1333$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$1333$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$1333$$$ is divisible by $$$19$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$23$$$.
Determine whether $$$1333$$$ is divisible by $$$23$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$29$$$.
Determine whether $$$1333$$$ is divisible by $$$29$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$31$$$.
Determine whether $$$1333$$$ is divisible by $$$31$$$.
It is divisible, thus, divide $$$1333$$$ by $$${\color{green}31}$$$: $$$\frac{1333}{31} = {\color{red}43}$$$.
The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.
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: $$$3999 = 3 \cdot 31 \cdot 43$$$.
Answer
The prime factorization is $$$3999 = 3 \cdot 31 \cdot 43$$$A.