Prime factorization of $$$4564$$$

Find the prime factorization of $$$4564$$$.

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

Determine whether $$$4564$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4564$$$ by $$${\color{green}2}$$$: $$$\frac{4564}{2} = {\color{red}2282}$$$.

Determine whether $$$2282$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2282$$$ by $$${\color{green}2}$$$: $$$\frac{2282}{2} = {\color{red}1141}$$$.

Determine whether $$$1141$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1141$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1141$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$1141$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1141$$$ by $$${\color{green}7}$$$: $$$\frac{1141}{7} = {\color{red}163}$$$.

The prime number $$${\color{green}163}$$$ has no other factors then $$$1$$$ and $$${\color{green}163}$$$: $$$\frac{163}{163} = {\color{red}1}$$$.

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: $$$4564 = 2^{2} \cdot 7 \cdot 163$$$.

The prime factorization is $$$4564 = 2^{2} \cdot 7 \cdot 163$$$A.