Prime factorization of $$$2209$$$
Your Input
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: $$$2209 = 47^{2}$$$.
Answer
The prime factorization is $$$2209 = 47^{2}$$$A.