# 533 and Level 4

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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## 3 thoughts on “533 and Level 4”

1. 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.)

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