# Prime factorization of $2200$

The calculator will find the prime factorization of $2200$, with steps shown.

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Find the prime factorization of $2200$.

### Solution

Start with the number $2$.

Determine whether $2200$ is divisible by $2$.

It is divisible, thus, divide $2200$ by ${\color{green}2}$: $\frac{2200}{2} = {\color{red}1100}$.

Determine whether $1100$ is divisible by $2$.

It is divisible, thus, divide $1100$ by ${\color{green}2}$: $\frac{1100}{2} = {\color{red}550}$.

Determine whether $550$ is divisible by $2$.

It is divisible, thus, divide $550$ by ${\color{green}2}$: $\frac{550}{2} = {\color{red}275}$.

Determine whether $275$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $275$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $275$ is divisible by $5$.

It is divisible, thus, divide $275$ by ${\color{green}5}$: $\frac{275}{5} = {\color{red}55}$.

Determine whether $55$ is divisible by $5$.

It is divisible, thus, divide $55$ by ${\color{green}5}$: $\frac{55}{5} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $2200 = 2^{3} \cdot 5^{2} \cdot 11$.

The prime factorization is $2200 = 2^{3} \cdot 5^{2} \cdot 11$A.