Prime factorization of $$$2208$$$

Find the prime factorization of $$$2208$$$.

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

Determine whether $$$2208$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2208$$$ by $$${\color{green}2}$$$: $$$\frac{2208}{2} = {\color{red}1104}$$$.

Determine whether $$$1104$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1104$$$ by $$${\color{green}2}$$$: $$$\frac{1104}{2} = {\color{red}552}$$$.

Determine whether $$$552$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$552$$$ by $$${\color{green}2}$$$: $$$\frac{552}{2} = {\color{red}276}$$$.

Determine whether $$$276$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$276$$$ by $$${\color{green}2}$$$: $$$\frac{276}{2} = {\color{red}138}$$$.

Determine whether $$$138$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$138$$$ by $$${\color{green}2}$$$: $$$\frac{138}{2} = {\color{red}69}$$$.

Determine whether $$$69$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$69$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$69$$$ by $$${\color{green}3}$$$: $$$\frac{69}{3} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$2208 = 2^{5} \cdot 3 \cdot 23$$$.

The prime factorization is $$$2208 = 2^{5} \cdot 3 \cdot 23$$$A.