Prime factorization of $$$3875$$$

Find the prime factorization of $$$3875$$$.

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

Determine whether $$$3875$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3875$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3875$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3875$$$ by $$${\color{green}5}$$$: $$$\frac{3875}{5} = {\color{red}775}$$$.

Determine whether $$$775$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$775$$$ by $$${\color{green}5}$$$: $$$\frac{775}{5} = {\color{red}155}$$$.

Determine whether $$$155$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$155$$$ by $$${\color{green}5}$$$: $$$\frac{155}{5} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$3875 = 5^{3} \cdot 31$$$.

The prime factorization is $$$3875 = 5^{3} \cdot 31$$$A.