1146 Mystery Level

This puzzle might start off easy enough, but soon afterward you will have to consider some serious logic in order to complete it. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1134-1147

Now let me tell you about the number 1146:

  • 1146 is a composite number.
  • Prime factorization: 1146 = 2 × 3 × 191
  • 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 1146 has exactly 8 factors.
  • Factors of 1146: 1, 2, 3, 6, 191, 382, 573, 1146
  • Factor pairs: 1146 = 1 × 1146, 2 × 573, 3 × 382, or 6 × 191
  • 1146 has no square factors that allow its square root to be simplified. √1146 ≈ 33.85262

1146 is a palindrome in two other bases:
It’s 14041 in BASE 5 because 1(5⁴) + 4(5³) + 0(5²) + 4(5¹) + 1(5⁰) = 1146,
and it’s 282 in BASE 22 because 2(22²) + 8(22) + 2(1) = 1146

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