Prime factorization of $$$3565$$$
Your Input
Find the prime factorization of $$$3565$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3565$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3565$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$3565$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$3565$$$ by $$${\color{green}5}$$$: $$$\frac{3565}{5} = {\color{red}713}$$$.
Determine whether $$$713$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$713$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$713$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$713$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$713$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$713$$$ is divisible by $$$19$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$23$$$.
Determine whether $$$713$$$ is divisible by $$$23$$$.
It is divisible, thus, divide $$$713$$$ by $$${\color{green}23}$$$: $$$\frac{713}{23} = {\color{red}31}$$$.
The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.
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: $$$3565 = 5 \cdot 23 \cdot 31$$$.
Answer
The prime factorization is $$$3565 = 5 \cdot 23 \cdot 31$$$A.