Prime factorization of $$$2605$$$
Your Input
Find the prime factorization of $$$2605$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2605$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$2605$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$2605$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$2605$$$ by $$${\color{green}5}$$$: $$$\frac{2605}{5} = {\color{red}521}$$$.
The prime number $$${\color{green}521}$$$ has no other factors then $$$1$$$ and $$${\color{green}521}$$$: $$$\frac{521}{521} = {\color{red}1}$$$.
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: $$$2605 = 5 \cdot 521$$$.
Answer
The prime factorization is $$$2605 = 5 \cdot 521$$$A.