Does prime factorization work for every number explain why or why not

Prime factorization only applies to integers greater than 2:

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 . 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 . 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.

c is the final answer! : )

24

step-by-step explanation: