Prime factorization of $$$3650$$$
Your Input
Find the prime factorization of $$$3650$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3650$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3650$$$ by $$${\color{green}2}$$$: $$$\frac{3650}{2} = {\color{red}1825}$$$.
Determine whether $$$1825$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1825$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1825$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1825$$$ by $$${\color{green}5}$$$: $$$\frac{1825}{5} = {\color{red}365}$$$.
Determine whether $$$365$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$365$$$ by $$${\color{green}5}$$$: $$$\frac{365}{5} = {\color{red}73}$$$.
The prime number $$${\color{green}73}$$$ has no other factors then $$$1$$$ and $$${\color{green}73}$$$: $$$\frac{73}{73} = {\color{red}1}$$$.
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: $$$3650 = 2 \cdot 5^{2} \cdot 73$$$.
Answer
The prime factorization is $$$3650 = 2 \cdot 5^{2} \cdot 73$$$A.