A Multiplication Based Logic Puzzle

Yes, 939 is a palindrome in base 10, but also all of its factors (1, 3, 313, and 939) are palindromes. It is also palindrome
32223 in BASE 4 because 3(4⁴) + 2(4³) + 2(4²) + 2(4¹) + 3(4⁰) = 939

Okay, that’s nice. Is there anything else special about 939?

The first ten decimal places of the cube root of 939 contain ALL ten digits 0 to 9. That’s unusual, and a reason why 939 is a special number. I made this gif to highlight its uniqueness.
Cube Root 939

make science GIFs like this at MakeaGif

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Thank you Stetson.edu for informing us of that amazing fact about 939’s cube root.

939 is also the hypotenuse of a Pythagorean triple:
75-936-939 which is 3 times (25-312-313)

  • 939 is a composite number.
  • Prime factorization: 939 = 3 × 313
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 939 has exactly 4 factors.
  • Factors of 939: 1, 3, 313, 939
  • Factor pairs: 939 = 1 × 939 or 3 × 313
  • 939 has no square factors that allow its square root to be simplified. √939 ≈ 30.64310689

 

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