Prime factorization of $$$529$$$
Your Input
Find the prime factorization of $$$529$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$529$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$529$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$529$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$529$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$529$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$529$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$529$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$529$$$ is divisible by $$$19$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$23$$$.
Determine whether $$$529$$$ is divisible by $$$23$$$.
It is divisible, thus, divide $$$529$$$ by $$${\color{green}23}$$$: $$$\frac{529}{23} = {\color{red}23}$$$.
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: $$$529 = 23^{2}$$$.
Answer
The prime factorization is $$$529 = 23^{2}$$$A.