Prime factorization of $$$572$$$

Find the prime factorization of $$$572$$$.

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

Determine whether $$$572$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$572$$$ by $$${\color{green}2}$$$: $$$\frac{572}{2} = {\color{red}286}$$$.

Determine whether $$$286$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$286$$$ by $$${\color{green}2}$$$: $$$\frac{286}{2} = {\color{red}143}$$$.

Determine whether $$$143$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$143$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$143$$$ by $$${\color{green}11}$$$: $$$\frac{143}{11} = {\color{red}13}$$$.

The prime number $$${\color{green}13}$$$ has no other factors then $$$1$$$ and $$${\color{green}13}$$$: $$$\frac{13}{13} = {\color{red}1}$$$.

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: $$$572 = 2^{2} \cdot 11 \cdot 13$$$.

The prime factorization is $$$572 = 2^{2} \cdot 11 \cdot 13$$$A.