Prime factorization of $$$3210$$$

Find the prime factorization of $$$3210$$$.

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

Determine whether $$$3210$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3210$$$ by $$${\color{green}2}$$$: $$$\frac{3210}{2} = {\color{red}1605}$$$.

Determine whether $$$1605$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1605$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1605$$$ by $$${\color{green}3}$$$: $$$\frac{1605}{3} = {\color{red}535}$$$.

Determine whether $$$535$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$535$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$535$$$ by $$${\color{green}5}$$$: $$$\frac{535}{5} = {\color{red}107}$$$.

The prime number $$${\color{green}107}$$$ has no other factors then $$$1$$$ and $$${\color{green}107}$$$: $$$\frac{107}{107} = {\color{red}1}$$$.

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: $$$3210 = 2 \cdot 3 \cdot 5 \cdot 107$$$.

The prime factorization is $$$3210 = 2 \cdot 3 \cdot 5 \cdot 107$$$A.