Prime factorization of $$$3030$$$

Find the prime factorization of $$$3030$$$.

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

Determine whether $$$3030$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3030$$$ by $$${\color{green}2}$$$: $$$\frac{3030}{2} = {\color{red}1515}$$$.

Determine whether $$$1515$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1515$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1515$$$ by $$${\color{green}3}$$$: $$$\frac{1515}{3} = {\color{red}505}$$$.

Determine whether $$$505$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$505$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$505$$$ by $$${\color{green}5}$$$: $$$\frac{505}{5} = {\color{red}101}$$$.

The prime number $$${\color{green}101}$$$ has no other factors then $$$1$$$ and $$${\color{green}101}$$$: $$$\frac{101}{101} = {\color{red}1}$$$.

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: $$$3030 = 2 \cdot 3 \cdot 5 \cdot 101$$$.

The prime factorization is $$$3030 = 2 \cdot 3 \cdot 5 \cdot 101$$$A.