Prime factorization of $$$2776$$$

Find the prime factorization of $$$2776$$$.

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

Determine whether $$$2776$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2776$$$ by $$${\color{green}2}$$$: $$$\frac{2776}{2} = {\color{red}1388}$$$.

Determine whether $$$1388$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1388$$$ by $$${\color{green}2}$$$: $$$\frac{1388}{2} = {\color{red}694}$$$.

Determine whether $$$694$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$694$$$ by $$${\color{green}2}$$$: $$$\frac{694}{2} = {\color{red}347}$$$.

The prime number $$${\color{green}347}$$$ has no other factors then $$$1$$$ and $$${\color{green}347}$$$: $$$\frac{347}{347} = {\color{red}1}$$$.

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: $$$2776 = 2^{3} \cdot 347$$$.

The prime factorization is $$$2776 = 2^{3} \cdot 347$$$A.