Prime factorization of $$$2979$$$

Find the prime factorization of $$$2979$$$.

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

Determine whether $$$2979$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2979$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2979$$$ by $$${\color{green}3}$$$: $$$\frac{2979}{3} = {\color{red}993}$$$.

Determine whether $$$993$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$993$$$ by $$${\color{green}3}$$$: $$$\frac{993}{3} = {\color{red}331}$$$.

The prime number $$${\color{green}331}$$$ has no other factors then $$$1$$$ and $$${\color{green}331}$$$: $$$\frac{331}{331} = {\color{red}1}$$$.

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: $$$2979 = 3^{2} \cdot 331$$$.

The prime factorization is $$$2979 = 3^{2} \cdot 331$$$A.