Prime factorization of $$$4470$$$

Find the prime factorization of $$$4470$$$.

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

Determine whether $$$4470$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4470$$$ by $$${\color{green}2}$$$: $$$\frac{4470}{2} = {\color{red}2235}$$$.

Determine whether $$$2235$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2235$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2235$$$ by $$${\color{green}3}$$$: $$$\frac{2235}{3} = {\color{red}745}$$$.

Determine whether $$$745$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$745$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$745$$$ by $$${\color{green}5}$$$: $$$\frac{745}{5} = {\color{red}149}$$$.

The prime number $$${\color{green}149}$$$ has no other factors then $$$1$$$ and $$${\color{green}149}$$$: $$$\frac{149}{149} = {\color{red}1}$$$.

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: $$$4470 = 2 \cdot 3 \cdot 5 \cdot 149$$$.

The prime factorization is $$$4470 = 2 \cdot 3 \cdot 5 \cdot 149$$$A.