A Multiplication Based Logic Puzzle

716 and Level 6

  • 716 is a composite number.
  • Prime factorization: 716 = 2 x 2 x 179, which can be written 716 = (2^2) x 179
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 716 has exactly 6 factors.
  • Factors of 716: 1, 2, 4, 179, 358, 716
  • Factor pairs: 716 = 1 x 716, 2 x 358, or 4 x 179
  • Taking the factor pair with the largest square number factor, we get √716 = (√4)(√179) = 2√179 ≈ 26.758176.

You may find this Candy Cane puzzle more challenging than sweet:

 

716 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-12-14

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Here are two more facts about the number 716:

86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 = 716; that’s 8 consecutive numbers.

716 is palindrome 282 in BASE 17; note that 2(17²) + 8(17) + 2(1) = 716

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716 Logic

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