Prime factorization of $$$3060$$$

Find the prime factorization of $$$3060$$$.

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

Determine whether $$$3060$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3060$$$ by $$${\color{green}2}$$$: $$$\frac{3060}{2} = {\color{red}1530}$$$.

Determine whether $$$1530$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1530$$$ by $$${\color{green}2}$$$: $$$\frac{1530}{2} = {\color{red}765}$$$.

Determine whether $$$765$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$765$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$765$$$ by $$${\color{green}3}$$$: $$$\frac{765}{3} = {\color{red}255}$$$.

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: $$$3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$$$.

The prime factorization is $$$3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$$$A.