Question

What is the prime factorization of $64$?

Answer 1

Determine the prime factorization of $64$.

Prime numbers are whole numbers greater than one that can only be divided equally by themselves and one.

Divide $64$ by only prime numbers to obtain the prime factorization.

The number $64$ is divided by $2$, which is a prime number.

$\begin{array}{rcl}64÷2& =& 32\\ & \Rightarrow & 32÷2=16\\ & \Rightarrow & 16÷2=8\\ & \Rightarrow & 8÷2=4\\ & \Rightarrow & 4÷2=2\\ & \Rightarrow & 2÷2=1\end{array}$

Thus, the prime factorization of $64$ is obtained as follows:

$\begin{array}{rcl}64& =& 2\times 2\times 2\times 2\times 2\times 2\\ & \Rightarrow & 64=2^6\end{array}$

Hence, the prime factorization of $64$ is $2^6$.