Prime factorization of $$$4136$$$

Find the prime factorization of $$$4136$$$.

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

Determine whether $$$4136$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4136$$$ by $$${\color{green}2}$$$: $$$\frac{4136}{2} = {\color{red}2068}$$$.

Determine whether $$$2068$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2068$$$ by $$${\color{green}2}$$$: $$$\frac{2068}{2} = {\color{red}1034}$$$.

Determine whether $$$1034$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1034$$$ by $$${\color{green}2}$$$: $$$\frac{1034}{2} = {\color{red}517}$$$.

Determine whether $$$517$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$517$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$517$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$517$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$517$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$517$$$ by $$${\color{green}11}$$$: $$$\frac{517}{11} = {\color{red}47}$$$.

The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.

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: $$$4136 = 2^{3} \cdot 11 \cdot 47$$$.

The prime factorization is $$$4136 = 2^{3} \cdot 11 \cdot 47$$$A.