how many natural numbers are there with 24 factors where 2,3 and 5 are the only prime factors?

1) 36
2) 27
3) 12
4) 9

• 24=2^3*3
  These powers have to be distributed in 3 places…
  A+b+c=3 has 10 soln
  X+y+z=1 has 3 soln
  Net =10*3=30 but here 2,2,6 is also included 3 times..hence ans =30-3=27
  
• 11 years agoHelpfull: Yes(1) No(2)
• number of factors =(m+1)*(n+1)*(c+1)
  24=2*3*4
  =2*2*6
  with prime numbers as 2,3 and 5. using permutation and combination
  2^1*3^2*5^3 can be arranged in 6 different ways
  similarly, 2^3*3^1*5^2 can be arranged in 6 different ways
  2^3*3^2*5^1 can be in 6 different ways.
  and 2^2*3^3*5^1 can be in 6 different ways.
  and similarly, 2*2*6 can be in 3 different ways.
  so 6+6+6+6+3=27
  
  
  
• 8 years agoHelpfull: Yes(0) No(1)