# Prime factorization of $2244$

The calculator will find the prime factorization of $2244$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $2244$.

### Solution

Start with the number $2$.

Determine whether $2244$ is divisible by $2$.

It is divisible, thus, divide $2244$ by ${\color{green}2}$: $\frac{2244}{2} = {\color{red}1122}$.

Determine whether $1122$ is divisible by $2$.

It is divisible, thus, divide $1122$ by ${\color{green}2}$: $\frac{1122}{2} = {\color{red}561}$.

Determine whether $561$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $561$ is divisible by $3$.

It is divisible, thus, divide $561$ by ${\color{green}3}$: $\frac{561}{3} = {\color{red}187}$.

Determine whether $187$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $187$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $187$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $187$ is divisible by $11$.

It is divisible, thus, divide $187$ by ${\color{green}11}$: $\frac{187}{11} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $2244 = 2^{2} \cdot 3 \cdot 11 \cdot 17$.

The prime factorization is $2244 = 2^{2} \cdot 3 \cdot 11 \cdot 17$A.