Number Divisibility

Important Basic Formulas in number divisibility:

  1. n(n + l)(2n + 1) is always divisible by 6.
  2. 32n leaves remainder = 1 when divided by 8
  3. n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9
  4. 102n + 1 + 1 is always divisible by 11
  5. n(n2- 1) is always divisible by 6
  6. n2+ n is always even
  7. 23n-1 is always divisible by 7
  8. 152n-1 +l is always divisible by 16
  9. n3 + 2n is always divisible by 3
  10. 34n – 4 3n is always divisible by 17
  11. n! + 1 is not divisible by any number between 2 and n(where n! = n (n – l)(n – 2)(n – 3)…….3.2.1)
  12. For eg 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800
  13. Product of n consecutive numbers is always divisible by n!.
  14. If n is a positive integer and p is a prime, then np – n is divisible by p

 


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