533 is the sum of consecutive primes two different ways: 173 + 179 + 181 = 533 = 101 + 103 + 107 + 109 + 113.

533 = (23^2) + (2^2), and 533 = (22^2) + (7^2)

533 is the hypotenuse of four Pythagorean triples. Some of the triples have a greatest common factor greater than one, and the rest are primitive. Which are which?

- 92-525-533
- 117-520-533
- 205-492-533
- 308-435-533

Print the puzzles or type the solution on this excel file: 10 Factors 2015-06-22

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- 533 is a composite number.
- Prime factorization: 533 = 13 x 41
- 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 533 has exactly 4 factors.
- Factors of 533: 1, 13, 41, 533
- Factor pairs: 533 = 1 x 533 or 13 x 41
- 533 has no square factors that allow its square root to be simplified. √533 ≈ 23.08679

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The Pythagorean triplets point is a neat one. I wasn’t aware of any numbers that were hypotenuses for so many triplets.

It’s really not all that unusual or even that many. For example 325 is the hypotenuse of seven Pythagorean triples.

I didn’t realize. I must have missed it. (Well, I was away from home a couple weeks ago.)