Prime factorization of $$$1038$$$

Find the prime factorization of $$$1038$$$.

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

Determine whether $$$1038$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1038$$$ by $$${\color{green}2}$$$: $$$\frac{1038}{2} = {\color{red}519}$$$.

Determine whether $$$519$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$519$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$519$$$ by $$${\color{green}3}$$$: $$$\frac{519}{3} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$1038 = 2 \cdot 3 \cdot 173$$$.

The prime factorization is $$$1038 = 2 \cdot 3 \cdot 173$$$A.