A Multiplication Based Logic Puzzle

638 and Level 3

638 is the sum of the four prime numbers from 151 to 167.

6 – 3 + 8 = 11. Thus 638 is divisible by 11.

638 is also the hypotenuse of the Pythagorean triple 440-462-638. What is the greatest common factor of those three numbers?

638 Puzzle

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

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  • 638 is a composite number.
  • Prime factorization: 638 = 2 x 11 x 29
  • 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 x 2 x 2 = 8. Therefore 638 has exactly 8 factors.
  • Factors of 638: 1, 2, 11, 22, 29, 58, 319, 638
  • Factor pairs: 638 = 1 x 638, 2 x 319, 11 x 58, or 22 x 29
  • 638 has no square factors that allow its square root to be simplified. √638 ≈ 25.25866.

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A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. (None of the factors are greater than 12.)  Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

638 Factors

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