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

• answer..25
  no. of factors of (a^m)(b^n) = (m+1)(n+1)
  now,
  16= 4*4 = (3+1)(3+1)
  suppose (2^3)(3^3) will be equal to 6^3
  so n = 6
  now, 6^4 = (2^4)(3^4)
  FACTOR = (4+1)(4+1) = 25
• 8 years agoHelpfull: Yes(3) No(0)
• given n^3 has 16 factors
  we know that x^k has k+1 factors
  =>n^3=(somevalue)^5*3=(some value)^15
  similalrly n^4=(somevalue)^5*4
  = 5*4=20+1 = 21 factors
• 8 years agoHelpfull: Yes(2) No(0)
• n^3 has 16 factor that is 4*4
  similarly n^4 has 25 factor as 5*5
  
• 8 years agoHelpfull: Yes(2) No(0)
• What is the right ans??
• 8 years agoHelpfull: Yes(0) No(0)
• n=8
  8^4
  25
• 8 years agoHelpfull: Yes(0) No(0)
• answer is 25 factors
• 8 years agoHelpfull: Yes(0) No(0)
• factors 16=4*4
  so,3,3 in cube,
  so n^4 3+1,3+1=4,4 so 4+1*4+4
  25.so answer is 25
• 8 years agoHelpfull: Yes(0) No(0)
• let us take n=2*x (you can take any number in place of 2)
  n^3 means 2^3 *x^3 so (3+1)*(3+1) =16 factors are present
  n^4 means 2^4 * x^4 so (4+1)*(4+1)=25 factors
• 8 years agoHelpfull: Yes(0) No(0)
• So, for Y=3, we have number of factors=16.
  Which means (3+1)^X=16=> X=2.
  
  Now putting Y=4, we get (Y+1)^X=(4+1)^2= 25 factors.
  Hence we can say that N has atmost 25 factors.
• 8 years agoHelpfull: Yes(0) No(0)