Question

What is the prime factorization of the number $8,788$?

Answer 1

Determine the prime factorization of $8,788$.

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

Divide $8,788$ by only prime numbers to obtain the prime factorization.

The number $8,788$ is divided by $2$, which is a prime number.

$\begin{array}{rcl}8788÷2& =& 4394\\ 4394÷2& =& 2197\end{array}$

Now, $2197$ is divided by $13$, which is a prime number.

$\begin{array}{rcl}2197÷13& =& 169\\ & \Rightarrow & 169÷13=13\\ & \Rightarrow & 13÷13=1\end{array}$

Thus, the prime factorization of $8,788$ is obtained as follows:

$\begin{array}{rcl}8,788& =& 2\times 2\times 13\times 13\times 13\\ & \Rightarrow & 90=2^2\times {13}^3\end{array}$

Hence, the prime factorization of $8,788$ is $\begin{array}{rcl}& & 2^2\times {13}^3\end{array}$.