Prime factorization of $$$2258$$$

Find the prime factorization of $$$2258$$$.

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

Determine whether $$$2258$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2258$$$ by $$${\color{green}2}$$$: $$$\frac{2258}{2} = {\color{red}1129}$$$.

The prime number $$${\color{green}1129}$$$ has no other factors then $$$1$$$ and $$${\color{green}1129}$$$: $$$\frac{1129}{1129} = {\color{red}1}$$$.

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: $$$2258 = 2 \cdot 1129$$$.

The prime factorization is $$$2258 = 2 \cdot 1129$$$A.