Prime factorization of $$$2180$$$

Find the prime factorization of $$$2180$$$.

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

Determine whether $$$2180$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2180$$$ by $$${\color{green}2}$$$: $$$\frac{2180}{2} = {\color{red}1090}$$$.

Determine whether $$$1090$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1090$$$ by $$${\color{green}2}$$$: $$$\frac{1090}{2} = {\color{red}545}$$$.

Determine whether $$$545$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$545$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$545$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$545$$$ by $$${\color{green}5}$$$: $$$\frac{545}{5} = {\color{red}109}$$$.

The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.

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: $$$2180 = 2^{2} \cdot 5 \cdot 109$$$.

The prime factorization is $$$2180 = 2^{2} \cdot 5 \cdot 109$$$A.