Prime factorization of $$$4256$$$

Find the prime factorization of $$$4256$$$.

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

Determine whether $$$4256$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4256$$$ by $$${\color{green}2}$$$: $$$\frac{4256}{2} = {\color{red}2128}$$$.

Determine whether $$$2128$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2128$$$ by $$${\color{green}2}$$$: $$$\frac{2128}{2} = {\color{red}1064}$$$.

Determine whether $$$1064$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1064$$$ by $$${\color{green}2}$$$: $$$\frac{1064}{2} = {\color{red}532}$$$.

Determine whether $$$532$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$532$$$ by $$${\color{green}2}$$$: $$$\frac{532}{2} = {\color{red}266}$$$.

Determine whether $$$266$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$266$$$ by $$${\color{green}2}$$$: $$$\frac{266}{2} = {\color{red}133}$$$.

Determine whether $$$133$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$133$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$133$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$133$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$133$$$ by $$${\color{green}7}$$$: $$$\frac{133}{7} = {\color{red}19}$$$.

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: $$$4256 = 2^{5} \cdot 7 \cdot 19$$$.

The prime factorization is $$$4256 = 2^{5} \cdot 7 \cdot 19$$$A.