463 and Level 5

463 is the sum of consecutive primes, too! Check the comments to see if any of my readers finds out what those consecutive primes are.

This Level 5 puzzle might be a little harder than usual. If you’ve solved a Level 5 puzzle before, see if you can meet this challenge!

463 Puzzle

Print the puzzles or type the solution on this excel file:  10 Factors 2015-04-13

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  • 463 is a prime number.
  • Prime factorization: 463 is prime.
  • The exponent of prime number 463 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 463 has exactly 2 factors.
  • Factors of 463: 1, 463
  • Factor pairs: 463 = 1 x 463
  • 463 has no square factors that allow its square root to be simplified. √463 ≈ 21.5174

How do we know that 463 is a prime number? If 463 were not a prime number, then it would be divisible by at least one prime number less than or equal to √463 ≈ 21.5174. Since 463 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 463 is a prime number.

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463 Logic

 

 

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6 thoughts on “463 and Level 5

    • Yes, this is the type of fun most people never experience.

      So far, at least person has met the challenge for the numbers 439, 440, 449, 457, 460, 462, and 463.

      No one typed in the consecutive primes for 431 and 432 because I gave clues that made finding the primes not much of a challenge, but the comments are still waiting for someone to type in the consecutive primes that total 442 and 456 (two different ways).

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