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!

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

—————————————————————————————————

• 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.

—————————————————————————————————