Prime factorization of $$$2140$$$

Find the prime factorization of $$$2140$$$.

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

Determine whether $$$2140$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2140$$$ by $$${\color{green}2}$$$: $$$\frac{2140}{2} = {\color{red}1070}$$$.

Determine whether $$$1070$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1070$$$ by $$${\color{green}2}$$$: $$$\frac{1070}{2} = {\color{red}535}$$$.

Determine whether $$$535$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$535$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$535$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$535$$$ by $$${\color{green}5}$$$: $$$\frac{535}{5} = {\color{red}107}$$$.

The prime number $$${\color{green}107}$$$ has no other factors then $$$1$$$ and $$${\color{green}107}$$$: $$$\frac{107}{107} = {\color{red}1}$$$.

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: $$$2140 = 2^{2} \cdot 5 \cdot 107$$$.

The prime factorization is $$$2140 = 2^{2} \cdot 5 \cdot 107$$$A.