A Multiplication Based Logic Puzzle

510 and Level 2

510 is the sum of consecutive prime numbers three different ways.

  1. 510 = 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79
  2. 510 = 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71
  3. 510 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67

510 is the hypotenuse of four Pythagorean triples, none of which are primitive:

  1. 78-504-510
  2. 216-462-510
  3. 240-450-510
  4. 306-408-510

Two of those triples have the same greatest common factor. Can you identify which ones they are?

510 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-06-01

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  • 510 is a composite number.
  • Prime factorization: 510 = 2 x 3 x 5 x 17
  • The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 x 2 = 16. Therefore 510 has exactly 16 factors.
  • Factors of 510: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
  • Factor pairs: 510 = 1 x 510, 2 x 255, 3 x 170, 5 x 102, 6 x 85, 10 x 51, 15 x 34, or 17 x 30
  • 510 has no square factors that allow its square root to be simplified. √510 ≈ 22.58317958

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510 Factors

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