1034 Find the Factors Challenge Puzzle

One of the things I really like about these Challenge puzzles is that you have to use logic. Guessing and checking just won’t work. Go ahead and give this puzzle a try!

Print the puzzles or type the solution in this excel file: 12 factors 1028-1034

Here are a few facts about the number 1034:

1 – 0 + 3 – 4 = 0, so 1034 can be evenly divided by 11.

Because 1034 = 2(47)(11), it is the short leg of a few Pythagorean triples including
1034-2088-2330 calculated from 2(47)(11), 47² – 11², 47² + 11²

  • 1034 is a composite number.
  • Prime factorization: 1034 = 2 × 11 × 47
  • 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 1034 has exactly 8 factors.
  • Factors of 1034: 1, 2, 11, 22, 47, 94, 517, 1034
  • Factor pairs: 1034 = 1 × 1034, 2 × 517, 11 × 94, or 22 × 47
  • 1034 has no square factors that allow its square root to be simplified. √1034 ≈ 32.15587

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