Prime factorization of $$$1112$$$

Find the prime factorization of $$$1112$$$.

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

Determine whether $$$1112$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1112$$$ by $$${\color{green}2}$$$: $$$\frac{1112}{2} = {\color{red}556}$$$.

Determine whether $$$556$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$556$$$ by $$${\color{green}2}$$$: $$$\frac{556}{2} = {\color{red}278}$$$.

Determine whether $$$278$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$278$$$ by $$${\color{green}2}$$$: $$$\frac{278}{2} = {\color{red}139}$$$.

The prime number $$${\color{green}139}$$$ has no other factors then $$$1$$$ and $$${\color{green}139}$$$: $$$\frac{139}{139} = {\color{red}1}$$$.

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: $$$1112 = 2^{3} \cdot 139$$$.

The prime factorization is $$$1112 = 2^{3} \cdot 139$$$A.