Prime factorization of $$$1048$$$

Find the prime factorization of $$$1048$$$.

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

Determine whether $$$1048$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1048$$$ by $$${\color{green}2}$$$: $$$\frac{1048}{2} = {\color{red}524}$$$.

Determine whether $$$524$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$524$$$ by $$${\color{green}2}$$$: $$$\frac{524}{2} = {\color{red}262}$$$.

Determine whether $$$262$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$262$$$ by $$${\color{green}2}$$$: $$$\frac{262}{2} = {\color{red}131}$$$.

The prime number $$${\color{green}131}$$$ has no other factors then $$$1$$$ and $$${\color{green}131}$$$: $$$\frac{131}{131} = {\color{red}1}$$$.

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: $$$1048 = 2^{3} \cdot 131$$$.

The prime factorization is $$$1048 = 2^{3} \cdot 131$$$A.