Prime factorization of $$$3667$$$
Your Input
Find the prime factorization of $$$3667$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3667$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3667$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$3667$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$3667$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$3667$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$3667$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$3667$$$ is divisible by $$$17$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$19$$$.
Determine whether $$$3667$$$ is divisible by $$$19$$$.
It is divisible, thus, divide $$$3667$$$ by $$${\color{green}19}$$$: $$$\frac{3667}{19} = {\color{red}193}$$$.
The prime number $$${\color{green}193}$$$ has no other factors then $$$1$$$ and $$${\color{green}193}$$$: $$$\frac{193}{193} = {\color{red}1}$$$.
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: $$$3667 = 19 \cdot 193$$$.
Answer
The prime factorization is $$$3667 = 19 \cdot 193$$$A.