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Here are all of the divisors of 1008: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. Actually, I think that one divisor is missing. Is there a fast way to figure out what it is?
Answer: Divisors occur in pairs. Look at the list. 1x1008=1008, 2x504=1008, 3x336=1008, 4x252=1008, etc. If the original number (1008) is not a square, then there should be an even number of pairs. If it is a square, then its square root (a factor) is paired with itself, and there are an odd number of pairs. 1008 is not a square, and I have listed an odd number (29) of divisors. So I was right; there is at least one missing divisor (assuming that the numbers that I listed are actually divisors). And we can start from both ends and pair up divisors and see which one does not have a mate. If we do that (I started to do that above) we find that 16 is not paired with a larger number. 1008/16=63. So 63 is the missing divisor.