# Prime factorization of $2209$

The calculator will find the prime factorization of $2209$, with steps shown.

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Find the prime factorization of $2209$.

### Solution

Start with the number $2$.

Determine whether $2209$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2209$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2209$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2209$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $2209$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $2209$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $2209$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $2209$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $2209$ is divisible by $23$.

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

The next prime number is $29$.

Determine whether $2209$ is divisible by $29$.

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

The next prime number is $31$.

Determine whether $2209$ is divisible by $31$.

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

The next prime number is $37$.

Determine whether $2209$ is divisible by $37$.

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

The next prime number is $41$.

Determine whether $2209$ is divisible by $41$.

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

The next prime number is $43$.

Determine whether $2209$ is divisible by $43$.

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

The next prime number is $47$.

Determine whether $2209$ is divisible by $47$.

It is divisible, thus, divide $2209$ by ${\color{green}47}$: $\frac{2209}{47} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

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: $2209 = 47^{2}$.

The prime factorization is $2209 = 47^{2}$A.