Prime factorization of $$$3508$$$

Find the prime factorization of $$$3508$$$.

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

Determine whether $$$3508$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3508$$$ by $$${\color{green}2}$$$: $$$\frac{3508}{2} = {\color{red}1754}$$$.

Determine whether $$$1754$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1754$$$ by $$${\color{green}2}$$$: $$$\frac{1754}{2} = {\color{red}877}$$$.

The prime number $$${\color{green}877}$$$ has no other factors then $$$1$$$ and $$${\color{green}877}$$$: $$$\frac{877}{877} = {\color{red}1}$$$.

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: $$$3508 = 2^{2} \cdot 877$$$.

The prime factorization is $$$3508 = 2^{2} \cdot 877$$$A.