What is the prime factorization of 125?

Oct 29, 2016

The prime factorization of $125$ is ${5}^{3}$.

Explanation:

To find the prime factorization, divide $125$ by only prime numbers. Remember that prime numbers are whole numbers greater than $1$ that are only evenly divisible by themselves and $1$.
{$2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53$, etc.}

Since $125$ ends in $5$, it is evenly divisible by $5$, which is a prime number. (How convenient!)

$125 \div 5 = 25$

$25$ now has to be factored into its prime factors.

$25 = 5 \cdot 5$

So, the prime factorization of $125$ is

$125 = 5 \cdot 5 \cdot 5 = {5}^{3}$