Prime factorization of $$$3125$$$

Find the prime factorization of $$$3125$$$.

Start with the number $$$2$$$.

Determine whether $$$3125$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$3125$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$3125$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3125$$$ by $$${\color{green}5}$$$: $$$\frac{3125}{5} = {\color{red}625}$$$.

Determine whether $$$625$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$625$$$ by $$${\color{green}5}$$$: $$$\frac{625}{5} = {\color{red}125}$$$.

Determine whether $$$125$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$125$$$ by $$${\color{green}5}$$$: $$$\frac{125}{5} = {\color{red}25}$$$.

Determine whether $$$25$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$25$$$ by $$${\color{green}5}$$$: $$$\frac{25}{5} = {\color{red}5}$$$.

The prime number $$${\color{green}5}$$$ has no other factors then $$$1$$$ and $$${\color{green}5}$$$: $$$\frac{5}{5} = {\color{red}1}$$$.

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: $$$3125 = 5^{5}$$$.

The prime factorization is $$$3125 = 5^{5}$$$A.