Prime factorization of $$$3090$$$

Find the prime factorization of $$$3090$$$.

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

Determine whether $$$3090$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3090$$$ by $$${\color{green}2}$$$: $$$\frac{3090}{2} = {\color{red}1545}$$$.

Determine whether $$$1545$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1545$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1545$$$ by $$${\color{green}3}$$$: $$$\frac{1545}{3} = {\color{red}515}$$$.

Determine whether $$$515$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$515$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$515$$$ by $$${\color{green}5}$$$: $$$\frac{515}{5} = {\color{red}103}$$$.

The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.

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: $$$3090 = 2 \cdot 3 \cdot 5 \cdot 103$$$.

The prime factorization is $$$3090 = 2 \cdot 3 \cdot 5 \cdot 103$$$A.