1210 Challenge Puzzle

Some of these Find the Factors Challenge puzzles are easier than others. This one is probably not one of the easier ones. Have fun with it anyway!

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Now I’ll share a few facts about the number 1210:

  • 1210 is a composite number.
  • Prime factorization: 1210 = 2 × 5 × 11 × 11, which can be written 1210 = 2 × 5 × 11²
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1210 has exactly 12 factors.
  • Factors of 1210: 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210
  • Factor pairs: 1210 = 1 × 1210, 2 × 605, 5 × 242, 10 × 121, 11 × 110, or 22 × 55,
  • Taking the factor pair with the largest square number factor, we get √1210 = (√121)(√10) = 11√10 ≈ 34.78505

1210 is the hypotenuse of a Pythagorean triple:
726-968-1210 which is (3-4-5) times 242

1210 is
1122211 in BASE 3
626 in BASE 14
181 in BASE 31

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