What the prime factors of 200

Start with 2, noting that 2 divides into 200 evenly. What's the next integer that also divides into 200 evenly? Not 3. 4? Yes. 5? Yes. And so on.

I get {2, 4, 5, 8, 10}. Of course 20 is a factor of 200, but not a prime factor.

8 and 10 are not prime. 8 = 2^3 and 10 = 2 and 5. But these factors {2, 5} have already been identified as prime factors of 200.

Thus, the prime factors of 200 are {2, 5}. Note that 200 = 2*100, or

2*4*25, or

2^3*5^2.