1310 Happy Birthday to My Brother, Andy

 

Today is my brother’s birthday. He likes puzzles so I’ve made him a tough, challenging one. Still, he’ll probably figure it out in no time. Happy birthday, Andy!

Like always, I’ll write what I’ve learned about a number. This time it’s 1310’s turn.

  • 1310 is a composite number.
  • Prime factorization: 1310 = 2 × 5 × 131
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1310 has exactly 8 factors.
  • Factors of 1310: 1, 2, 5, 10, 131, 262, 655, 1310
  • Factor pairs: 1310 = 1 × 1310, 2 × 655, 5 × 262, or 10 × 131
  • 1310 has no square factors that allow its square root to be simplified. √1310 ≈ 36.19392

1310 is the hypotenuse of a Pythagorean triple:
786-1048-1310 which is (3-4-5) times 262

 

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