Prime factorization only applies to integers greater than 2:
[tex]\{2, 3, 4, 5, 6, 7,\ldots\}[/tex]
If you only consider these numbers, then yes: you can factor all of them.
Starting from 2, every other number is either prime, or divisibile by a prime we already found. Let's see a little bit of steps.
We begin with 2. It's divisible only by 1 and itself, so it's prime.
Then we have 3. It's divisible only by 1 and itself, so it's prime.
Then we have 4. It's divisibile by 2, so we can break into [tex]2\times 2[/tex]. The "remaining" 2 is prime, and we're done with the factorization.
Then we have 5. It's divisible only by 1 and itself, so it's prime.
Then we have 6. It's divisibile by 2, so we can break into [tex]2\times 3[/tex]. The "remaining" 3 is prime, and we're done with the factorization.
And you go on like this. The idea is that you either find a new prime or you can break the number into smaller pieces that you have already identified and factored.
