Prime factorization of $$$3562$$$
Your Input
Find the prime factorization of $$$3562$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3562$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3562$$$ by $$${\color{green}2}$$$: $$$\frac{3562}{2} = {\color{red}1781}$$$.
Determine whether $$$1781$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1781$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1781$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1781$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$1781$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$1781$$$ is divisible by $$$13$$$.
It is divisible, thus, divide $$$1781$$$ by $$${\color{green}13}$$$: $$$\frac{1781}{13} = {\color{red}137}$$$.
The prime number $$${\color{green}137}$$$ has no other factors then $$$1$$$ and $$${\color{green}137}$$$: $$$\frac{137}{137} = {\color{red}1}$$$.
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: $$$3562 = 2 \cdot 13 \cdot 137$$$.
Answer
The prime factorization is $$$3562 = 2 \cdot 13 \cdot 137$$$A.