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

• solve by using prime factorization
  consider a term 6.
  6^3 -> can be written as -> 2^3 * 3^3
  then by factor rule , (3+1)*(3+1)=16
  therefore,
  6^4=(2^4)*(3^4) ---> (4+1)*(4+1) = 25
  Ans: 25
  
• 11 years agoHelpfull: Yes(17) No(1)
• 21 or 25
  m+1=16 (m+1)(n+1)=16
  m=15 (m+1)(n+1)= 4*4
  a^15=N^3 m= 3 n= 3
  N=a^5 a^3*b^3= N^3
  N^4=a^20 a*b= N
  factors=21 a^4*b^4= N^4
  factors=25
• 11 years agoHelpfull: Yes(5) No(7)
• if n=6 then n3 = 216 so n = 6 and 216which is having 3 3's and 3 2's so n4 = 1296 which is having 4 2's and 4 3's so factors equals to 25
  
• 11 years agoHelpfull: Yes(5) No(4)
• m+1=16.
  a^15=n^3
  n=a^5
  n^4=a^20
  no: of factors is 21
• 11 years agoHelpfull: Yes(4) No(1)
• (3+1)(3+1)=16..this is for n^3..for n^4 it will be (3+1+(3/3))(3+1+(3/3))=5*5=25
• 11 years agoHelpfull: Yes(2) No(0)
• n=6 and n^4=6^4=(2*3)^4=5*5=25
• 11 years agoHelpfull: Yes(1) No(0)
• lets take n as 8
  then 4^3*2^3=(3+1)*(3+1)=16 factors
  same as 4^4*2^4=(4+1)*(4+1)=25 factors
  whatever may be the value of n just apply this method
• 11 years agoHelpfull: Yes(1) No(0)
• 21 will be the correct answer !!!
• 11 years agoHelpfull: Yes(0) No(1)