Prime factorization of $$$4560$$$

Find the prime factorization of $$$4560$$$.

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

Determine whether $$$4560$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4560$$$ by $$${\color{green}2}$$$: $$$\frac{4560}{2} = {\color{red}2280}$$$.

Determine whether $$$2280$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2280$$$ by $$${\color{green}2}$$$: $$$\frac{2280}{2} = {\color{red}1140}$$$.

Determine whether $$$1140$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1140$$$ by $$${\color{green}2}$$$: $$$\frac{1140}{2} = {\color{red}570}$$$.

Determine whether $$$570$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$570$$$ by $$${\color{green}2}$$$: $$$\frac{570}{2} = {\color{red}285}$$$.

Determine whether $$$285$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$285$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$285$$$ by $$${\color{green}3}$$$: $$$\frac{285}{3} = {\color{red}95}$$$.

Determine whether $$$95$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$95$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$95$$$ by $$${\color{green}5}$$$: $$$\frac{95}{5} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19$$$.

The prime factorization is $$$4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19$$$A.