Prime factorization of $$$4430$$$

Find the prime factorization of $$$4430$$$.

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

Determine whether $$$4430$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4430$$$ by $$${\color{green}2}$$$: $$$\frac{4430}{2} = {\color{red}2215}$$$.

Determine whether $$$2215$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2215$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2215$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$2215$$$ by $$${\color{green}5}$$$: $$$\frac{2215}{5} = {\color{red}443}$$$.

The prime number $$${\color{green}443}$$$ has no other factors then $$$1$$$ and $$${\color{green}443}$$$: $$$\frac{443}{443} = {\color{red}1}$$$.

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: $$$4430 = 2 \cdot 5 \cdot 443$$$.

The prime factorization is $$$4430 = 2 \cdot 5 \cdot 443$$$A.