Prime factorization of $$$4616$$$

Find the prime factorization of $$$4616$$$.

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

Determine whether $$$4616$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4616$$$ by $$${\color{green}2}$$$: $$$\frac{4616}{2} = {\color{red}2308}$$$.

Determine whether $$$2308$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2308$$$ by $$${\color{green}2}$$$: $$$\frac{2308}{2} = {\color{red}1154}$$$.

Determine whether $$$1154$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1154$$$ by $$${\color{green}2}$$$: $$$\frac{1154}{2} = {\color{red}577}$$$.

The prime number $$${\color{green}577}$$$ has no other factors then $$$1$$$ and $$${\color{green}577}$$$: $$$\frac{577}{577} = {\color{red}1}$$$.

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: $$$4616 = 2^{3} \cdot 577$$$.

The prime factorization is $$$4616 = 2^{3} \cdot 577$$$A.