Prime factorization of $$$2778$$$

Find the prime factorization of $$$2778$$$.

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

Determine whether $$$2778$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2778$$$ by $$${\color{green}2}$$$: $$$\frac{2778}{2} = {\color{red}1389}$$$.

Determine whether $$$1389$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$1389$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1389$$$ by $$${\color{green}3}$$$: $$$\frac{1389}{3} = {\color{red}463}$$$.

The prime number $$${\color{green}463}$$$ has no other factors then $$$1$$$ and $$${\color{green}463}$$$: $$$\frac{463}{463} = {\color{red}1}$$$.

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: $$$2778 = 2 \cdot 3 \cdot 463$$$.

The prime factorization is $$$2778 = 2 \cdot 3 \cdot 463$$$A.