Prime factorization of $$$3500$$$
Your Input
Find the prime factorization of $$$3500$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3500$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3500$$$ by $$${\color{green}2}$$$: $$$\frac{3500}{2} = {\color{red}1750}$$$.
Determine whether $$$1750$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1750$$$ by $$${\color{green}2}$$$: $$$\frac{1750}{2} = {\color{red}875}$$$.
Determine whether $$$875$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$875$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$875$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$875$$$ by $$${\color{green}5}$$$: $$$\frac{875}{5} = {\color{red}175}$$$.
Determine whether $$$175$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$175$$$ by $$${\color{green}5}$$$: $$$\frac{175}{5} = {\color{red}35}$$$.
Determine whether $$$35$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.
The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.
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: $$$3500 = 2^{2} \cdot 5^{3} \cdot 7$$$.
Answer
The prime factorization is $$$3500 = 2^{2} \cdot 5^{3} \cdot 7$$$A.