# Prime factorization of $2208$

The calculator will find the prime factorization of $2208$, with steps shown.

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Find the prime factorization of $2208$.

### Solution

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.