A Multiplication Based Logic Puzzle

  • 767 is a composite number.
  • Prime factorization: 767 = 13 x 59
  • 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 767 has exactly 4 factors.
  • Factors of 767: 1, 13, 59, 767
  • Factor pairs: 767 = 1 x 767 or 13 x 59
  • 767 has no square factors that allow its square root to be simplified. √767 ≈ 27.69476.

767-factor-pairs

Because 13 is one of its factors, 767 is the hypotenuse of Pythagorean triple 295-708-767, but 767 will never be part of the solution to one of these Pythagorean triple puzzles because it is greater than 100. Every side and hypotenuse in these puzzles must be a whole number less than 100. Together the numbers in the puzzle must form Pythagorean triples. Can you solve the puzzle?

767 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2016-02-25

————————————-

Here’s a little more about the number 767:

767 is a palindrome in two different bases:

  • 767 in BASE 10; note that 7(100) + 6(10) + 7(7) = 767.
  • 2B2 in BASE 17 (B = 11 base 10); note that 2(289) + 11(17) + 2(1) = 767.

Wikipedia informs us that 767 is also the 9th Thabit number.

————————————-

Advertisements

Comments on: "767 is the hypotenuse of a Pythagorean triple, but…" (2)

  1. Hmm….makes me wonder id we’ll see more Thabit numbers from you. One more? Two More? I’d be happy with 53 more, but that’s for another story..

    Liked by 1 person

  2. I expect to write about a few more, but 53 more would be impossible unless I start writing about numbers out of sequence.

    Like

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