Prime factorization of $$$3890$$$

Find the prime factorization of $$$3890$$$.

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

Determine whether $$$3890$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3890$$$ by $$${\color{green}2}$$$: $$$\frac{3890}{2} = {\color{red}1945}$$$.

Determine whether $$$1945$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1945$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1945$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1945$$$ by $$${\color{green}5}$$$: $$$\frac{1945}{5} = {\color{red}389}$$$.

The prime number $$${\color{green}389}$$$ has no other factors then $$$1$$$ and $$${\color{green}389}$$$: $$$\frac{389}{389} = {\color{red}1}$$$.

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: $$$3890 = 2 \cdot 5 \cdot 389$$$.

The prime factorization is $$$3890 = 2 \cdot 5 \cdot 389$$$A.