Find the maximum value of n such that
42*57*92*91*52*62*63*64*65*66*67 is perfectly divisible by 42^n.

• 42=7*6;
  57=3*19;
  92=4*23;
  91=7*13;
  52=4*13;
  62=2*31;
  63=7*3*3;
  64=2^6;
  65=5*13;
  66=6*11;
  so, if the given xpressn is decomposed as above,we then find that 7^3 is a factor of the above expression.And from the above factorization,we also find that 6^3 also divides the given expression.
  since 6 & 7 r co-prime to each other,i.e,as 6 & 7 doesn't hav any comn factor,so,(6*7)^3=(42)^3 will also divide the above expression.
  
  So, the maximum possible value of n=3 ..
• 11 years agoHelpfull: Yes(6) No(0)
• n=1
  since none of the other numbers are divisible by 42
• 11 years agoHelpfull: Yes(0) No(3)