1298 Another Mystery

Hint #1: Which two clues will use both of the nines?
Hint #2: Which two clues will use both of the sixes?

6, 7, 8, or 12, two of them will use the 1’s. One of those 1’s will be in the first column. They both can’t be. That fact was important when I worked to solve this puzzle.

It won’t be easy, but why don’t you give it a try?

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

It won’t help to solve the puzzle, but I’ll share some information now about our puzzle number, 1298:

  • 1298 is a composite number.
  • Prime factorization: 1298 = 2 × 11 × 59
  • 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 1298 has exactly 8 factors.
  • Factors of 1298: 1, 2, 11, 22, 59, 118, 649, 1298
  • Factor pairs: 1298 = 1 × 1298, 2 × 649, 11 × 118, or 22 × 59
  • 1298 has no square factors that allow its square root to be simplified. √1298 ≈ 36.02777

1298 is the sum of four consecutive prime numbers:
313 + 317 + 331 + 337 = 1298

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