Prime factorization of $$$4000$$$
Your Input
Find the prime factorization of $$$4000$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$4000$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$4000$$$ by $$${\color{green}2}$$$: $$$\frac{4000}{2} = {\color{red}2000}$$$.
Determine whether $$$2000$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2000$$$ by $$${\color{green}2}$$$: $$$\frac{2000}{2} = {\color{red}1000}$$$.
Determine whether $$$1000$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1000$$$ by $$${\color{green}2}$$$: $$$\frac{1000}{2} = {\color{red}500}$$$.
Determine whether $$$500$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$500$$$ by $$${\color{green}2}$$$: $$$\frac{500}{2} = {\color{red}250}$$$.
Determine whether $$$250$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$250$$$ by $$${\color{green}2}$$$: $$$\frac{250}{2} = {\color{red}125}$$$.
Determine whether $$$125$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$125$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$125$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$125$$$ by $$${\color{green}5}$$$: $$$\frac{125}{5} = {\color{red}25}$$$.
Determine whether $$$25$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$25$$$ by $$${\color{green}5}$$$: $$$\frac{25}{5} = {\color{red}5}$$$.
The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.
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: $$$4000 = 2^{5} \cdot 5^{3}$$$.
Answer
The prime factorization is $$$4000 = 2^{5} \cdot 5^{3}$$$A.