Prime factorization of $$$4524$$$

Find the prime factorization of $$$4524$$$.

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

Determine whether $$$4524$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4524$$$ by $$${\color{green}2}$$$: $$$\frac{4524}{2} = {\color{red}2262}$$$.

Determine whether $$$2262$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2262$$$ by $$${\color{green}2}$$$: $$$\frac{2262}{2} = {\color{red}1131}$$$.

Determine whether $$$1131$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1131$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1131$$$ by $$${\color{green}3}$$$: $$$\frac{1131}{3} = {\color{red}377}$$$.

Determine whether $$$377$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$377$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$377$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$377$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$377$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$377$$$ by $$${\color{green}13}$$$: $$$\frac{377}{13} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$4524 = 2^{2} \cdot 3 \cdot 13 \cdot 29$$$.

The prime factorization is $$$4524 = 2^{2} \cdot 3 \cdot 13 \cdot 29$$$A.