n is a natural number and n 3 has 16 factors then find the no of factors of n 4

let n=6 or 10 so n^3=6^3 or 10^3
6^3=2^3*3^3, no. of factors=(3+1)*(3+1)=16
10^3=2^3*5^3, no. of factors=(3+1)*(3+1)=16
so no. of factors of 6^4=2^4*3^4=(4+1)*(4+1)=25
hence no. of factors of n^4=25
ans 25
10 years agoHelpfull: Yes(13) No(1)
n^3 has 16 factors

=> 16= 2*8 or 4* 4

=> (1+1)* (7+1) or ( 3+1)*(3+1)
=> i.e. (p+1)*(q+1)
we will consider only 4*4 because if n has two factors a*b
then, n^3 has a^3 * b^3 factors.

so, n^4 = a^4 *b^4
=> (4+1)*(4+1)
= 5*5
= 25 ans.
10 years agoHelpfull: Yes(5) No(4)
if n=a*b where a & b are prime no.
then given situation is possible in 2 ways
n=a^3*b^3 or a^15(b=1) (in both the cases no. of factor =16)
n^4 have either 25/ 21 factors
10 years agoHelpfull: Yes(1) No(3)
2^16=65536
(65536)^1/3=40
then 40^4=2560000
2560000=2^7*10*10*10*10=2^11*5^4
total factor=(11+4)=15
10 years agoHelpfull: Yes(0) No(9)
n^3=(a*b)^3=a^3*b^3 factor=4*4=16
n^4=(a*b)^4=a^4*b^4
factor=5*5=25
10 years agoHelpfull: Yes(0) No(1)

n is a natural number and n^3 has 16 factors then find the no of factors of n^4