A Multiplication Based Logic Puzzle

Since 394 is an even number not divisible by 4, it can’t be part of a primitive Pythagorean triple. Scroll down past the puzzle to see its factors and its two non-primitive triples.

394 Puzzle

Print the puzzles or type the factors on this excel file: 10 Factors 2015-02-16

  • 394 is a composite number.
  • Prime factorization: 394 = 2 x 197
  • 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 394 has exactly 4 factors.
  • Factors of 394: 1, 2, 197, 394
  • Factor pairs: 394 = 1 x 394 or 2 x 197
  • 394 has no square factors that allow its square root to be simplified. √394 ≈ 19.849

To find Pythagorean triples with the number 394, first divide it in half to get 197. Since 197 is 14² + 1, we know it is the hypotenuse of the triple formed from 2(14 x 1), 14² – 1, and 14² + 1 or (28-195-197). If we multiply that triple by 2, we get (56-390-394).

Prime number 197 is also the short leg of the primitive Pythagorean triple, (197-19404-19405). Doubling each element of that triple gives us (394-38808-38810).

394 Factors

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