469 is the short leg in the Pythagorean triple 469-1608-1675. What is the greatest common factor of those three numbers? Hint: Don’t let the larger numbers scare you; the greatest common factor is a factor of 469, the smallest of those three numbers, and its factors are listed below the puzzle.
Print the puzzles or type the solution on this excel file: 12 Factors 2015-04-20
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- 469 is a composite number.
- Prime factorization: 469 = 7 x 67
- 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 469 has exactly 4 factors.
- Factors of 469: 1, 7, 67, 469
- Factor pairs: 469 = 1 x 469 or 7 x 67
- 469 has no square factors that allow its square root to be simplified. √469 ≈ 21.6564
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Yes I was scared until I read your hint.
You made this one quite easy..
Is it unusual for Pythagorean triplets to a have common factor?
That’s a very good question!
If the Pythagorean triple is primitive, the greatest common factor will be 1.
However, if it is not a primitive, the three numbers will always have a greatest common factor that is greater than 1.
I think I’ll write a post or two about this topic. Thanks!
So it’s all or nothing!?!
I look forward to your post about this. I’m especially curious about the lingo: is there an opposite word for the primitive in terms of Pythagorean triplets? I’ll wait for your post to find out. thank you.
As far as I can tell, the opposite of primitive is simply non-primitive.
Thank you for your curiosity!