Prime factorization of $$$4004$$$
Your Input
Find the prime factorization of $$$4004$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4004$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4004$$$ by $$${\color{green}2}$$$: $$$\frac{4004}{2} = {\color{red}2002}$$$.
Determine whether $$$2002$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2002$$$ by $$${\color{green}2}$$$: $$$\frac{2002}{2} = {\color{red}1001}$$$.
Determine whether $$$1001$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1001$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1001$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1001$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$1001$$$ by $$${\color{green}7}$$$: $$$\frac{1001}{7} = {\color{red}143}$$$.
Determine whether $$$143$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$143$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$143$$$ by $$${\color{green}11}$$$: $$$\frac{143}{11} = {\color{red}13}$$$.
The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.
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: $$$4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$$$.
Answer
The prime factorization is $$$4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13$$$A.