Prime factorization of $$$3054$$$

Find the prime factorization of $$$3054$$$.

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

Determine whether $$$3054$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3054$$$ by $$${\color{green}2}$$$: $$$\frac{3054}{2} = {\color{red}1527}$$$.

Determine whether $$$1527$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1527$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1527$$$ by $$${\color{green}3}$$$: $$$\frac{1527}{3} = {\color{red}509}$$$.

The prime number $$${\color{green}509}$$$ has no other factors then $$$1$$$ and $$${\color{green}509}$$$: $$$\frac{509}{509} = {\color{red}1}$$$.

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: $$$3054 = 2 \cdot 3 \cdot 509$$$.

The prime factorization is $$$3054 = 2 \cdot 3 \cdot 509$$$A.