Prime factorization of $$$3344$$$

Find the prime factorization of $$$3344$$$.

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

Determine whether $$$3344$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3344$$$ by $$${\color{green}2}$$$: $$$\frac{3344}{2} = {\color{red}1672}$$$.

Determine whether $$$1672$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1672$$$ by $$${\color{green}2}$$$: $$$\frac{1672}{2} = {\color{red}836}$$$.

Determine whether $$$836$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$836$$$ by $$${\color{green}2}$$$: $$$\frac{836}{2} = {\color{red}418}$$$.

Determine whether $$$418$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$418$$$ by $$${\color{green}2}$$$: $$$\frac{418}{2} = {\color{red}209}$$$.

Determine whether $$$209$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$209$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$209$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$209$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$209$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$209$$$ by $$${\color{green}11}$$$: $$$\frac{209}{11} = {\color{red}19}$$$.

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: $$$3344 = 2^{4} \cdot 11 \cdot 19$$$.

The prime factorization is $$$3344 = 2^{4} \cdot 11 \cdot 19$$$A.