n is an natural number,if n^3 is having 16 factors then how many factors does n^4 have?

• taking n=6.n^3 will be 216.Prime factors of 216=2^3*3^3.so (3+1)*(3+1)=16.n^4=1296.it can be written as 2^4*3^4.again, (4+1)*(4+1)=25.
• 11 years agoHelpfull: Yes(30) No(6)
• suppose n has 1+x no of factors..
  then n*n will have 1+x+x no of factors..
  similarly n*n*n will have 1+x+x+x no of factors..
  hence from eqn ..3x+1=16
  x=5.
  now calculate for 4x+1=21 factors
  
• 11 years agoHelpfull: Yes(11) No(3)
• (5*5)=25...
• 11 years agoHelpfull: Yes(7) No(6)
• lets take an example (2^5)^3--- the factors for this term is 16.
  Similary,(2^5)^4---- the factor is 21
  21 is the answer...
• 11 years agoHelpfull: Yes(1) No(8)
• putting n=7 we get n^3=216
  factorizing 216 apply formula (1+m)(1+n) we get factors =16
  similarly for n^4=1296 we get factors=25
• 11 years agoHelpfull: Yes(1) No(0)