Prime factorization of $$$3112$$$

Find the prime factorization of $$$3112$$$.

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

Determine whether $$$3112$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3112$$$ by $$${\color{green}2}$$$: $$$\frac{3112}{2} = {\color{red}1556}$$$.

Determine whether $$$1556$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1556$$$ by $$${\color{green}2}$$$: $$$\frac{1556}{2} = {\color{red}778}$$$.

Determine whether $$$778$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$778$$$ by $$${\color{green}2}$$$: $$$\frac{778}{2} = {\color{red}389}$$$.

The prime number $$${\color{green}389}$$$ has no other factors then $$$1$$$ and $$${\color{green}389}$$$: $$$\frac{389}{389} = {\color{red}1}$$$.

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: $$$3112 = 2^{3} \cdot 389$$$.

The prime factorization is $$$3112 = 2^{3} \cdot 389$$$A.