Prime factorization of $$$4540$$$

Find the prime factorization of $$$4540$$$.

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

Determine whether $$$4540$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4540$$$ by $$${\color{green}2}$$$: $$$\frac{4540}{2} = {\color{red}2270}$$$.

Determine whether $$$2270$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2270$$$ by $$${\color{green}2}$$$: $$$\frac{2270}{2} = {\color{red}1135}$$$.

Determine whether $$$1135$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1135$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1135$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1135$$$ by $$${\color{green}5}$$$: $$$\frac{1135}{5} = {\color{red}227}$$$.

The prime number $$${\color{green}227}$$$ has no other factors then $$$1$$$ and $$${\color{green}227}$$$: $$$\frac{227}{227} = {\color{red}1}$$$.

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: $$$4540 = 2^{2} \cdot 5 \cdot 227$$$.

The prime factorization is $$$4540 = 2^{2} \cdot 5 \cdot 227$$$A.