Prime factorization of $$$4098$$$

Find the prime factorization of $$$4098$$$.

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

Determine whether $$$4098$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4098$$$ by $$${\color{green}2}$$$: $$$\frac{4098}{2} = {\color{red}2049}$$$.

Determine whether $$$2049$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2049$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2049$$$ by $$${\color{green}3}$$$: $$$\frac{2049}{3} = {\color{red}683}$$$.

The prime number $$${\color{green}683}$$$ has no other factors then $$$1$$$ and $$${\color{green}683}$$$: $$$\frac{683}{683} = {\color{red}1}$$$.

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: $$$4098 = 2 \cdot 3 \cdot 683$$$.

The prime factorization is $$$4098 = 2 \cdot 3 \cdot 683$$$A.