1461 and Level 6

Today’s Puzzle:

Look at all the clues in this level 6 puzzle. Can you deduce the logic needed to begin solving it? Deduce it correctly, then solving the rest of the puzzle will be a breeze.

Factors of 1461:

  • 1461 is a composite number.
  • Prime factorization: 1461 = 3 × 487
  • 1461 has no exponents greater than 1 in its prime factorization, so √1461 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1461 has exactly 4 factors.
  • The factors of 1461 are outlined with their factor pair partners in the graphic below.

Another Fact about 1461:

1461 is the difference of two squares in two different ways:
731² – 730² = 1461
245² – 242² = 1461

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