A Multiplication Based Logic Puzzle

838 is a palindrome in base 10. Is it a palindrome in any other bases? Yes, two others.

  • 262 BASE 19 because 2(19²) + 6(19¹) + 2(19º) = 838
  • 141 BASE 27 because 1(27²) + 4(27¹) + 1(27º) = 838

There is only one way 838 can be written as the sum of consecutive numbers:

  • 208 + 209 + 210 + 211 = 838

Print the puzzles or type the solution on this excel file: 10-factors-835-842

  • 838 is a composite number.
  • Prime factorization: 838 = 2 × 419
  • 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 838 has exactly 4 factors.
  • Factors of 838: 1, 2, 419, 838
  • Factor pairs: 838 = 1 × 838 or 2 × 419
  • 838 has no square factors that allow its square root to be simplified. √838 ≈ 28.9482

 

 

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