Prime factorization of $$$3605$$$
Your Input
Find the prime factorization of $$$3605$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3605$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$3605$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$3605$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$3605$$$ by $$${\color{green}5}$$$: $$$\frac{3605}{5} = {\color{red}721}$$$.
Determine whether $$$721$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$721$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$721$$$ by $$${\color{green}7}$$$: $$$\frac{721}{7} = {\color{red}103}$$$.
The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.
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: $$$3605 = 5 \cdot 7 \cdot 103$$$.
Answer
The prime factorization is $$$3605 = 5 \cdot 7 \cdot 103$$$A.