Prime factorization of $$$3138$$$

Find the prime factorization of $$$3138$$$.

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

Determine whether $$$3138$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3138$$$ by $$${\color{green}2}$$$: $$$\frac{3138}{2} = {\color{red}1569}$$$.

Determine whether $$$1569$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1569$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1569$$$ by $$${\color{green}3}$$$: $$$\frac{1569}{3} = {\color{red}523}$$$.

The prime number $$${\color{green}523}$$$ has no other factors then $$$1$$$ and $$${\color{green}523}$$$: $$$\frac{523}{523} = {\color{red}1}$$$.

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: $$$3138 = 2 \cdot 3 \cdot 523$$$.

The prime factorization is $$$3138 = 2 \cdot 3 \cdot 523$$$A.