A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???

1) 729
2) 629
3) 329
4) some other option

• Let a,b,c be three prime no.
  since the no. of perfect square as a factor is 125
  which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
  so power must be 0,2,4,6,8
  thereby 5*5*5=125
  Since no. of cube as a factor is 27
  therefore power in the prime no. will be in the multiple of 3
  so power are 0,3,6
  hence the no. N=a^8*b^8*c^8
  hence total no. of factor is (8+1)(8+1)(8+1)=729
• 10 years agoHelpfull: Yes(0) No(0)