# 485 and Level 5

485 is the hypotenuse of four Pythagorean triples. Which ones are primitive and which ones aren’t?

• 44-483-485
• 93-476-485
• 291-388-485
• 325-360-485

Print the puzzles or type the solution on this excel file: 12 Factors 2015-05-04

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• 485 is a composite number.
• Prime factorization: 485 = 5 x 97
• 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 485 has exactly 4 factors.
• Factors of 485: 1, 5, 97, 485
• Factor pairs: 485 = 1 x 485 or 5 x 97
• 485 has no square factors that allow its square root to be simplified. √485 ≈ 22.0227155

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## 2 thoughts on “485 and Level 5”

1. This one is for me, right?
Okay, 44-483-485 doesn’t seem like it’s even worth playing with: primitive for sure.

93-476-485 likely primitive as well ( can’t fathom that 476 and 485 have any common factors).

325-360-485, well, are all multiples of 5, so it won’t be primitive (how am I doing?)

291-388-485: now this is the interesting one. seems 291 doesn’t have many factors, but it divides it by 3, and you get a 97, which, if you’ve done your math right in this post, also goes neatly into 485 (thank you) so 291-388-485 is not primitive!

What confounds me most about all this is that 485 is the hypotenuse of four Pythagorean triples. It just never occurred to me that a number could be the hypotenuse of more than one Pythagorean triplet.

• Thank you for recognizing that this problem was just for you! You got everything right, too!

If the hypotenuse of a Pythagorean triple is a prime number, then it will not be the hypotenuse of any other Pythagorean triple. However, if the hypotenuse is a composite number, it might be the hypotenuse of other triplets as well.

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