Prime factorization of $$$3500$$$

Find the prime factorization of $$$3500$$$.

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: $$$3500 = 2^{2} \cdot 5^{3} \cdot 7$$$.

The prime factorization is $$$3500 = 2^{2} \cdot 5^{3} \cdot 7$$$A.