help me

 

   Find the largest positive integer $n$ such that $n^3$ divides 15.     

 

   Well, it’s obvious that every number will divide 15.     

   But assuming the problem means evenly divisible,     

   then the only solution is n = 1.     

 

   Proof:  The quotient must be an integer with no remainder.     

 

   When n = 1, then n³ = 1, thus 15 / 1 = 15      This quotient does satisfy the stipulation.     

             n = 2, then n³ = 8, thus 15 / 8 = 1 R7   Having a remaider disqualifies the solution.     

             n = 3, then n³ = 27    This and all larger numbers produce a non-integer quotient.     

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