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

• correct answer is 21.
  let n = 32 which is 2^5
  then (2^5)^3 = 2^15 which has (15+1)=16 factors
  similarly (2^5)^4 = 2^20 which has (20+1) = 21 factors.
• 11 years agoHelpfull: Yes(21) No(8)
• say no is 4= 2^1 * 2^1
  then n^3= 4^3 =2^3 * 2^3 then no of factors = (3+1) *(3+1) =16
  therefore for n^4 = 4^4= 2^4 * 2^4
  then no of factors = (4+1)*(4+1)= 25 ..
  thus answer is 25.
  
  
• 11 years agoHelpfull: Yes(17) No(9)
• 25 can also be the answer if n is expressed as product to two primes.
  ex: take n = 6 = 3*2
  now n^3 = 3^3*2^3. therefore no. of factors = 4*4= 16
  now n^4 = 3^4*2^4. therefore no. of factors = 5*5 = 25
• 11 years agoHelpfull: Yes(5) No(0)
• ans would be 25
• 11 years agoHelpfull: Yes(4) No(3)
• n=32
  n^3 has 16 factors so,32^3=2^15 factors= (15+1)=16.then,
  n^4 has 32^4=2^20=(20+1)=21 factors.
  
• 11 years agoHelpfull: Yes(3) No(0)
• wat r the options??
  
  
• 11 years agoHelpfull: Yes(0) No(7)
• answer is 25
• 11 years agoHelpfull: Yes(0) No(0)
• if n = 2^5,
  We have (2^5)^3=>2^15=>16 ways!!!
  
  So, now putting the value of n we get 2^20 => 21 factorials.
• 11 years agoHelpfull: Yes(0) No(0)