Prime factorization of $$$2826$$$

Find the prime factorization of $$$2826$$$.

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

Determine whether $$$2826$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2826$$$ by $$${\color{green}2}$$$: $$$\frac{2826}{2} = {\color{red}1413}$$$.

Determine whether $$$1413$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1413$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1413$$$ by $$${\color{green}3}$$$: $$$\frac{1413}{3} = {\color{red}471}$$$.

Determine whether $$$471$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$471$$$ by $$${\color{green}3}$$$: $$$\frac{471}{3} = {\color{red}157}$$$.

The prime number $$${\color{green}157}$$$ has no other factors then $$$1$$$ and $$${\color{green}157}$$$: $$$\frac{157}{157} = {\color{red}1}$$$.

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: $$$2826 = 2 \cdot 3^{2} \cdot 157$$$.

The prime factorization is $$$2826 = 2 \cdot 3^{2} \cdot 157$$$A.