Prime factorization of $$$2040$$$

Find the prime factorization of $$$2040$$$.

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

Determine whether $$$2040$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2040$$$ by $$${\color{green}2}$$$: $$$\frac{2040}{2} = {\color{red}1020}$$$.

Determine whether $$$1020$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1020$$$ by $$${\color{green}2}$$$: $$$\frac{1020}{2} = {\color{red}510}$$$.

Determine whether $$$510$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$510$$$ by $$${\color{green}2}$$$: $$$\frac{510}{2} = {\color{red}255}$$$.

Determine whether $$$255$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$255$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$255$$$ by $$${\color{green}3}$$$: $$$\frac{255}{3} = {\color{red}85}$$$.

Determine whether $$$85$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$85$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$85$$$ by $$${\color{green}5}$$$: $$$\frac{85}{5} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17$$$.

The prime factorization is $$$2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17$$$A.