Prime factorization of $$$4056$$$

Find the prime factorization of $$$4056$$$.

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

Determine whether $$$4056$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4056$$$ by $$${\color{green}2}$$$: $$$\frac{4056}{2} = {\color{red}2028}$$$.

Determine whether $$$2028$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2028$$$ by $$${\color{green}2}$$$: $$$\frac{2028}{2} = {\color{red}1014}$$$.

Determine whether $$$1014$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1014$$$ by $$${\color{green}2}$$$: $$$\frac{1014}{2} = {\color{red}507}$$$.

Determine whether $$$507$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$507$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$507$$$ by $$${\color{green}3}$$$: $$$\frac{507}{3} = {\color{red}169}$$$.

Determine whether $$$169$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$169$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$169$$$ by $$${\color{green}13}$$$: $$$\frac{169}{13} = {\color{red}13}$$$.

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: $$$4056 = 2^{3} \cdot 3 \cdot 13^{2}$$$.

The prime factorization is $$$4056 = 2^{3} \cdot 3 \cdot 13^{2}$$$A.