n is a natural number and n^3 has 16 factors then how many factors can n^4 have?

• The correct answer will be 25
  
  suppose n^3= a^3*b^3
  
  Therefore by using formula to know total factors (3+1)*(3+1)=4*4=16 as it was given in question only...
  
  Now by using above concept we can write..
  
  n^4 = c^4*d^4
  
  so we will get (4+1)*(4+1) = 25
• 11 years agoHelpfull: Yes(40) No(4)
• 21 or 25
  
  16 = 1*8 or 4*4
  => n^3 is of the form a^15 or a^3 * b^3
  
  1) If n^3 = a^15 => n^4 = a^20
  => Number of factors = 21
  
  2) If n^3 = a^3 * b^3 => n^4 = a^4 * b^4
  => Number of factors = 25
• 11 years agoHelpfull: Yes(10) No(10)
• If n = 2^5 => n^3 = 2^15 which has 16 factors
  => n^4 = 2^20
  => 21 factors
  
  
• 11 years agoHelpfull: Yes(2) No(2)
• if n^3 has 16 factors
  then n^4 has to have 17 factors
  e.i one extra factor
  this extra factor is n^4 itself.
  we can seed examples using small values for n like 2,3...
• 11 years agoHelpfull: Yes(1) No(9)
• 21
  n^3=16 factors(1+3(5factors))
• 11 years agoHelpfull: Yes(1) No(1)
• it will be 17 n^2 means n*n
  
  why r u guys getting it complex
• 11 years agoHelpfull: Yes(1) No(1)
• hi kunal ....aj ka puzzle banaya :)
• 11 years agoHelpfull: Yes(0) No(6)