n is a number such that 2n has 28 factors and 3n has 30 factors.
then how many factors will 6n have?

• 2n has 28 factors.
  No of factors of a^p*B^q = (P+1)(q+1)....
  28=4*7=(3+1)(6+1) ie. 2n= (3^3)*(2^6)
  
  3n has 30 factors
  30=5*6=(4+1)(5+1) ie 3n=(3^4)*(2^5)
  
  Above values of 2n and 3n indicate that
  n=(2^5)*(3^3)
  »6n=(2^6)*(3^4)
  Therefore, number of factors of 6n= (6+1)(4+1)=35
• 9 years agoHelpfull: Yes(4) No(1)
• LCM (28,30) = 420
• 9 years agoHelpfull: Yes(1) No(2)
• here 2n has 28 factors and 3n has 30 factors so 6n =2n*3n so 28*30 factors are possible but here repititative factors should be removed.so by taking L.C.M the repititative factors are removed so ans is 2*14*15 i.e 420
• 9 years agoHelpfull: Yes(0) No(2)