1424 Logic and Fear

Should this puzzle excite fear in you or anyone else? The logical answer is no, of course not. Logic can also help you to find the solution, so don’t be afraid, give it a try!

Print the puzzles or type the solution in this excel file: 12 Factors 1419-1429

Finding the factors of 1424 shouldn’t bring fear to you either:

  • 1424 is a composite number.
  • Prime factorization: 1424 = 2 × 2 × 2 × 2 × 89, which can be written 1424 = 2⁴ × 89
  • 1424 has at least one exponent greater than 1 in its prime factorization so √1424 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1424 = (√16)(√89) = 4√89
  • The exponents in the prime factorization are 4 and 1. Adding one to each exponent and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 1424 has exactly 10 factors.
  • The factors of 1424 are outlined with their factor pair partners in the graphic below.

1424 is the sum of two squares:
32² + 20² = 1424

1424 is the hypotenuse of a Pythagorean triple:
624-1280-1424 calculated from 32² – 20², 2(32)(20), 32² + 20²

 

 

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