533 and Level 4

533 is the sum of consecutive primes two different ways: 173 + 179 + 181 = 533 = 101 + 103 + 107 + 109 + 113.

533 = (23^2) + (2^2), and 533 = (22^2) + (7^2)

533 is the hypotenuse of four Pythagorean triples. Some of the triples have a greatest common factor greater than one, and the rest are primitive. Which are which?

  • 92-525-533
  • 117-520-533
  • 205-492-533
  • 308-435-533

533 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-06-22

—————————————————————————————————

  • 533 is a composite number.
  • Prime factorization: 533 = 13 x 41
  • 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 533 has exactly 4 factors.
  • Factors of 533: 1, 13, 41, 533
  • Factor pairs: 533 = 1 x 533 or 13 x 41
  • 533 has no square factors that allow its square root to be simplified. √533 ≈ 23.08679

—————————————————————————————————

533 Logic

Advertisements

3 thoughts on “533 and Level 4

Leave a Reply