Prime factorization of $$$4446$$$

Find the prime factorization of $$$4446$$$.

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

Determine whether $$$4446$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4446$$$ by $$${\color{green}2}$$$: $$$\frac{4446}{2} = {\color{red}2223}$$$.

Determine whether $$$2223$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2223$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2223$$$ by $$${\color{green}3}$$$: $$$\frac{2223}{3} = {\color{red}741}$$$.

Determine whether $$$741$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$741$$$ by $$${\color{green}3}$$$: $$$\frac{741}{3} = {\color{red}247}$$$.

Determine whether $$$247$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$247$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$247$$$ by $$${\color{green}13}$$$: $$$\frac{247}{13} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4446 = 2 \cdot 3^{2} \cdot 13 \cdot 19$$$.

The prime factorization is $$$4446 = 2 \cdot 3^{2} \cdot 13 \cdot 19$$$A.