Prime factorization of $$$1980$$$

Find the prime factorization of $$$1980$$$.

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

Determine whether $$$1980$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1980$$$ by $$${\color{green}2}$$$: $$$\frac{1980}{2} = {\color{red}990}$$$.

Determine whether $$$990$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$990$$$ by $$${\color{green}2}$$$: $$$\frac{990}{2} = {\color{red}495}$$$.

Determine whether $$$495$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$495$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$495$$$ by $$${\color{green}3}$$$: $$$\frac{495}{3} = {\color{red}165}$$$.

Determine whether $$$165$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$165$$$ by $$${\color{green}3}$$$: $$$\frac{165}{3} = {\color{red}55}$$$.

Determine whether $$$55$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$55$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$55$$$ by $$${\color{green}5}$$$: $$$\frac{55}{5} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11$$$.

The prime factorization is $$$1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11$$$A.