Answer
$500 = 2\cdot 2\cdot 5\cdot 5\cdot 5$
Work Step by Step
The $\textit{prime factorization}$ of a number is obtained by writing the number as a product of primes.
To determine the prime factorization of $500$ we write the number as a product of factors and continue the process until all factors are prime numbers.
We start by writing $500$ as a product of two numbers: because the ones digit is even, $500$ is divisible by $2$:
$500=2\cdot 250$.
The number $2$ is prime, but $250$ is not. Because the ones digit is even, $250$ is divisible by $2$, so $250=2\cdot 125$:
$500=2\cdot 2\cdot 125$.
As $125$ is not a prime number and its ones digit is $0$ or $5$, it follows that $125$ is divisible by $5$, so $125=5\cdot 25$:
$500=2\cdot 2\cdot 5\cdot 25$.
As $25$ is not a prime number we write: $25=5\cdot 5$ and we have:
$500=2\cdot 2\cdot 5\cdot 5\cdot 5$.
Now each factor is a prime number, therefore the prime factorization of $500$ is $2\cdot 2\cdot 5\cdot 5\cdot 5$.
