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2013 Math Kangaroo

Problem 1

Problem 1 · 2013 Math Kangaroo Easy
Number Theory factorizationdivisibility

Which of the numbers is not a factor of \(200013 - 2013\)?

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Answer: D — 7
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Hint 1 of 2
Pull out the common piece first: both terms share a factor of 2013.
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Hint 2 of 2
Factor the result fully into primes, then check which listed number is missing.
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Approach: factor the difference and test each candidate divisor
  1. Factor out 2013: 200013 − 2013 = 198000.
  2. Break it down: 198000 = 198 × 1000 = (2 · 9 · 11) × (8 · 125), so the primes are 2, 3, 5, and 11.
  3. So 2, 3, 5 and 11 all divide it — but 7 does not.
  4. The number that is not a factor is 7.
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