A Multiplication Based Logic Puzzle

874 and Level 6

874 is the sum of the first 23 prime numbers:

  • 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 = 874

ALL of 874’s prime factors were included in that list.

Print the puzzles or type the solution on this excel file: 12 factors 864-874

  • 874 is a composite number.
  • Prime factorization: 874 = 2 × 19 × 23
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 874 has exactly 8 factors.
  • Factors of 874: 1, 2, 19, 23, 38, 46, 437, 874
  • Factor pairs: 874 = 1 × 874, 2 × 437, 19 × 46, or 23 × 38
  • 874 has no square factors that allow its square root to be simplified. √874 ≈ 29.56349.

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