Prime factorization of $$$1000$$$

Find the prime factorization of $$$1000$$$.

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

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: $$$1000 = 2^{3} \cdot 5^{3}$$$.

The prime factorization is $$$1000 = 2^{3} \cdot 5^{3}$$$A.