A Multiplication Based Logic Puzzle

549 and Level 6

549 is the hypotenuse of the Pythagorean triple 99-540-549. What is the greatest common factor of those three numbers?

549 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-07-06

—————————————————————————————————

  • 549 is a composite number.
  • Prime factorization: 549 = 3 x 3 x 61, which can be written 549 = (3^2) x 61
  • 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 549 has exactly 6 factors.
  • Factors of 549: 1, 3, 9, 61, 183, 549
  • Factor pairs: 549 = 1 x 549, 3 x 183, or 9 x 61
  • Taking the factor pair with the largest square number factor, we get √549 = (√9)(√61) = 3√61 ≈ 23.430749

—————————————————————————————————

549 Logic

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Tag Cloud