Answer
$588 = 2\cdot 2\cdot 3\cdot 7\cdot 7$
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 $588$ we write the number as a product of factors and continue the process until all factors are prime numbers.
We start by writing $588$ as a product of two numbers: because the ones digit is even, $588$ is divisible by $2$:
$588=2\cdot 294$.
The number $2$ is prime, but $294$ is not. Because the ones digit is even, $294$ is divisible by $2$, so $294=2\cdot 147$:
$588=2\cdot 2\cdot 147$.
As $147$ is not a prime number and the sum of its digits is $1+4+7=12$ divisible by $3$, it follows that $147$ is divisible by $3$, so $147=3\cdot 49$:
$588=2\cdot 2\cdot 3\cdot 49$.
As $49$ is not a prime number we write: $49=7\cdot 7$ and we have:
$588=2\cdot 2\cdot 3\cdot 7\cdot 7$.
Now each factor is a prime number, therefore the prime factorization of $588$ is $2\cdot 2\cdot 3\cdot 7\cdot 7$.
