Prime factorization of $$$4140$$$

Find the prime factorization of $$$4140$$$.

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

Determine whether $$$4140$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4140$$$ by $$${\color{green}2}$$$: $$$\frac{4140}{2} = {\color{red}2070}$$$.

Determine whether $$$2070$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2070$$$ by $$${\color{green}2}$$$: $$$\frac{2070}{2} = {\color{red}1035}$$$.

Determine whether $$$1035$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1035$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1035$$$ by $$${\color{green}3}$$$: $$$\frac{1035}{3} = {\color{red}345}$$$.

Determine whether $$$345$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$345$$$ by $$${\color{green}3}$$$: $$$\frac{345}{3} = {\color{red}115}$$$.

Determine whether $$$115$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$115$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$115$$$ by $$${\color{green}5}$$$: $$$\frac{115}{5} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23$$$.

The prime factorization is $$$4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23$$$A.