Prime factorization of $$$1536$$$

Find the prime factorization of $$$1536$$$.

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

Determine whether $$$1536$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1536$$$ by $$${\color{green}2}$$$: $$$\frac{1536}{2} = {\color{red}768}$$$.

Determine whether $$$768$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$768$$$ by $$${\color{green}2}$$$: $$$\frac{768}{2} = {\color{red}384}$$$.

Determine whether $$$384$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$384$$$ by $$${\color{green}2}$$$: $$$\frac{384}{2} = {\color{red}192}$$$.

Determine whether $$$192$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$192$$$ by $$${\color{green}2}$$$: $$$\frac{192}{2} = {\color{red}96}$$$.

Determine whether $$$96$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$96$$$ by $$${\color{green}2}$$$: $$$\frac{96}{2} = {\color{red}48}$$$.

Determine whether $$$48$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$48$$$ by $$${\color{green}2}$$$: $$$\frac{48}{2} = {\color{red}24}$$$.

Determine whether $$$24$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$24$$$ by $$${\color{green}2}$$$: $$$\frac{24}{2} = {\color{red}12}$$$.

Determine whether $$$12$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$12$$$ by $$${\color{green}2}$$$: $$$\frac{12}{2} = {\color{red}6}$$$.

Determine whether $$$6$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$6$$$ by $$${\color{green}2}$$$: $$$\frac{6}{2} = {\color{red}3}$$$.

The prime number $$${\color{green}3}$$$ has no other factors then $$$1$$$ and $$${\color{green}3}$$$: $$$\frac{3}{3} = {\color{red}1}$$$.

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: $$$1536 = 2^{9} \cdot 3$$$.

The prime factorization is $$$1536 = 2^{9} \cdot 3$$$A.