Prime factorization of $$$2588$$$

Find the prime factorization of $$$2588$$$.

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

Determine whether $$$2588$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2588$$$ by $$${\color{green}2}$$$: $$$\frac{2588}{2} = {\color{red}1294}$$$.

Determine whether $$$1294$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1294$$$ by $$${\color{green}2}$$$: $$$\frac{1294}{2} = {\color{red}647}$$$.

The prime number $$${\color{green}647}$$$ has no other factors then $$$1$$$ and $$${\color{green}647}$$$: $$$\frac{647}{647} = {\color{red}1}$$$.

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: $$$2588 = 2^{2} \cdot 647$$$.

The prime factorization is $$$2588 = 2^{2} \cdot 647$$$A.