Prime factorization of $$$2748$$$

Find the prime factorization of $$$2748$$$.

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

Determine whether $$$2748$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2748$$$ by $$${\color{green}2}$$$: $$$\frac{2748}{2} = {\color{red}1374}$$$.

Determine whether $$$1374$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1374$$$ by $$${\color{green}2}$$$: $$$\frac{1374}{2} = {\color{red}687}$$$.

Determine whether $$$687$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$687$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$687$$$ by $$${\color{green}3}$$$: $$$\frac{687}{3} = {\color{red}229}$$$.

The prime number $$${\color{green}229}$$$ has no other factors then $$$1$$$ and $$${\color{green}229}$$$: $$$\frac{229}{229} = {\color{red}1}$$$.

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: $$$2748 = 2^{2} \cdot 3 \cdot 229$$$.

The prime factorization is $$$2748 = 2^{2} \cdot 3 \cdot 229$$$A.