A Multiplication Based Logic Puzzle

639 and Level 4

639 is the sum of the 20 prime numbers from 2 to 71, its largest prime factor.

639 is made from 3 numbers that are divisible by 3 so 639 is divisible by 3 AND by 9.

Puzzle #639 has a tricky clue in it, but I’m sure you can still solve it.

639 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-10-05

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  • 639 is a composite number.
  • Prime factorization: 639 = 3 x 3 x 71, which can be written 639 = (3^2) x 71
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 639 has exactly 6 factors.
  • Factors of 639: 1, 3, 9, 71, 213, 639
  • Factor pairs: 639 = 1 x 639, 3 x 213, or 9 x 71
  • Taking the factor pair with the largest square number factor, we get √639 = (√9)(√71) = 3√71 ≈ 25.278449.

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639 Logic

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