1026 One Last Mystery

I made a week’s worth of mystery level puzzles, and today’s puzzle is the last one in the set. Find the Factors of the clues in this puzzle by using logic and your knowledge of the multiplication table. It may not be easy for you, but give it a try anyway. If you find it too difficult, I will soon publish some more easier-level puzzles.

Print the puzzles or type the solution in this excel file: 10-factors-1019-1027

Now let me share a few facts about the number 1026:

1026 is the sum of the fourteen prime numbers from 43 to 103.

I like the way 1026 looks when it is written in these other bases:
It’s 2002 in BASE 8,
396 in BASE 17,
330 in BASE 18,
1G1 in BASE 25 (G is 16 base 10), and
123 in BASE 31

  • 1026 is a composite number.
  • Prime factorization: 1026 = 2 × 3 × 3 × 3 × 19, which can be written 1026 = 2 × 3³ × 19
  • The exponents in the prime factorization are 1, 3, and 1. Adding one to each and multiplying we get (1 + 1)(3 + 1)(1 + 1) = 2 × 4 × 2 = 16. Therefore 1026 has exactly 16 factors.
  • Factors of 1026: 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026
  • Factor pairs: 1026 = 1 × 1026, 2 × 513, 3 × 342, 6 × 171, 9 × 114, 18 × 57, 19 × 54, or 27 × 38
  • Taking the factor pair with the largest square number factor, we get √1026 = (√9)(√114) = 3√114 ≈ 32.03123

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