Answer
$300 = 2\cdot 2\cdot 3\cdot 5\cdot 5$
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 $300$ we write the number as a product of factors and continue the process until all factors are prime numbers.
We start by writing $300$ as a product of two numbers: because the ones digit is even, $300$ is divisible by $2$:
$300=2\cdot 150$.
The number $2$ is prime, but $150$ is not. Because the ones digit is even, $150$ is divisible by $2$, so $150=2\cdot 75$:
$300=2\cdot 2\cdot 75$.
As $75$ is not a prime number and the sum of its digits is $7+5=12$ divisible by $3$, it follows that $75$ is divisible by $3$, so $75=3\cdot 25$:
$300=2\cdot 2\cdot 3\cdot 25$.
As $25$ is not a prime number we write: $25=5\cdot 5$ and we have:
$300=2\cdot 2\cdot 3\cdot 5\cdot 5$.
Now each factor is a prime number, therefore the prime factorization of $300$ is $2\cdot 2\cdot 3\cdot 5\cdot 5$.
