A Multiplication Based Logic Puzzle

633 and Level 5

  • 633 = 210 + 211 + 212 (three consecutive numbers)
  • 633 = 209 + 211 + 213 (three consecutive odd numbers)
  • 633 = 199 + 211 + 223 (three consecutive prime numbers)

Each of the sums above has 3 numbers, and 3 is a prime factor of 633. The middle number in each of the sums is 211 which is the other prime factor of 633.

Each of its two prime factors is 104 away from their average, 107.

Thus (107^2) – (104^2) = 633

The numbers in 633’s other factor pair are 1 and 633, and they are each 316 away from their average, 317.

Thus (317^2) – (316^2) = 633

633 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-09-28

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  • 633 is a composite number.
  • Prime factorization: 633 = 3 x 211
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 633 has exactly 4 factors.
  • Factors of 633: 1, 3, 211, 633
  • Factor pairs: 633 = 1 x 633 or 3 x 211
  • 633 has no square factors that allow its square root to be simplified. √633 ≈ 25.15949.

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633 Logic

 

 

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