Prime factorization of $$$2814$$$

Find the prime factorization of $$$2814$$$.

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

Determine whether $$$2814$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2814$$$ by $$${\color{green}2}$$$: $$$\frac{2814}{2} = {\color{red}1407}$$$.

Determine whether $$$1407$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1407$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1407$$$ by $$${\color{green}3}$$$: $$$\frac{1407}{3} = {\color{red}469}$$$.

Determine whether $$$469$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$469$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$469$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$469$$$ by $$${\color{green}7}$$$: $$$\frac{469}{7} = {\color{red}67}$$$.

The prime number $$${\color{green}67}$$$ has no other factors then $$$1$$$ and $$${\color{green}67}$$$: $$$\frac{67}{67} = {\color{red}1}$$$.

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: $$$2814 = 2 \cdot 3 \cdot 7 \cdot 67$$$.

The prime factorization is $$$2814 = 2 \cdot 3 \cdot 7 \cdot 67$$$A.