Prime factorization of $$$2306$$$

Find the prime factorization of $$$2306$$$.

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

Determine whether $$$2306$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2306$$$ by $$${\color{green}2}$$$: $$$\frac{2306}{2} = {\color{red}1153}$$$.

The prime number $$${\color{green}1153}$$$ has no other factors then $$$1$$$ and $$${\color{green}1153}$$$: $$$\frac{1153}{1153} = {\color{red}1}$$$.

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: $$$2306 = 2 \cdot 1153$$$.

The prime factorization is $$$2306 = 2 \cdot 1153$$$A.