Prime factorization of $$$4422$$$

Find the prime factorization of $$$4422$$$.

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

Determine whether $$$4422$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4422$$$ by $$${\color{green}2}$$$: $$$\frac{4422}{2} = {\color{red}2211}$$$.

Determine whether $$$2211$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2211$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2211$$$ by $$${\color{green}3}$$$: $$$\frac{2211}{3} = {\color{red}737}$$$.

Determine whether $$$737$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$737$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$737$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$737$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$737$$$ by $$${\color{green}11}$$$: $$$\frac{737}{11} = {\color{red}67}$$$.

The prime number $$${\color{green}67}$$$ has no other factors then $$$1$$$ and $$${\color{green}67}$$$: $$$\frac{67}{67} = {\color{red}1}$$$.

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: $$$4422 = 2 \cdot 3 \cdot 11 \cdot 67$$$.

The prime factorization is $$$4422 = 2 \cdot 3 \cdot 11 \cdot 67$$$A.