Prime factorization of $$$3048$$$

Find the prime factorization of $$$3048$$$.

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

Determine whether $$$3048$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3048$$$ by $$${\color{green}2}$$$: $$$\frac{3048}{2} = {\color{red}1524}$$$.

Determine whether $$$1524$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1524$$$ by $$${\color{green}2}$$$: $$$\frac{1524}{2} = {\color{red}762}$$$.

Determine whether $$$762$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$762$$$ by $$${\color{green}2}$$$: $$$\frac{762}{2} = {\color{red}381}$$$.

Determine whether $$$381$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$381$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$381$$$ by $$${\color{green}3}$$$: $$$\frac{381}{3} = {\color{red}127}$$$.

The prime number $$${\color{green}127}$$$ has no other factors then $$$1$$$ and $$${\color{green}127}$$$: $$$\frac{127}{127} = {\color{red}1}$$$.

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: $$$3048 = 2^{3} \cdot 3 \cdot 127$$$.

The prime factorization is $$$3048 = 2^{3} \cdot 3 \cdot 127$$$A.