Q. Find the no of divisor 1080 excluding the divisor which are perfect square?

Option
a) 28
b) 29
c) 30
d) 31

• no of divisors of 1080=2^3*5^1*3^3
  then no of factors = 4*2*4=32
  excluding perfect square factors=(2^0+2^2)(3^0+3^2)(5^0)=2*2*1=4
  so ans=32-4=28 i.e. a
• 11 years agoHelpfull: Yes(28) No(2)
• 28 is the answer
  (2^0+2^1+2^2+2^3)(3^0+3^1+3^2+3^3)(5^0+5^1)
  2^0.3^0.5^0=1
  2^2=4,
  3^2=9,
  2^2.3^2=36
  
  total number of factors
  32
  32-4=28 factors
  
• 11 years agoHelpfull: Yes(14) No(2)
• 1080=2^3 x 3^3 x 5^1
  So, Number of divisors/factors = (3+1) x (3+1) x (1+1) = 32
  Out of all the factors 1, 4(2^2), 9(3^3) and 36 (9 x 4) are perfect Squares.
  So the answer is 32-4 = 28.
• 10 years agoHelpfull: Yes(9) No(0)
• perform factorization
  1080=(2^3)*(3^3)*5
  no of factor=(2^0+2^1+2^2+2^3)*(3^0+3^1+3^2+3^3)*(5^0+5^1)
  therfore no of factor which will divide 1080 are
  4*4*2=32,from wich 4 and 9 are perfect square that divide 1080 therfore
  32-2=30 is answer
• 11 years agoHelpfull: Yes(2) No(10)
• @akash...how u calculae the no of factors...ie 32..explain
• 10 years agoHelpfull: Yes(1) No(1)
• brother.its ok if we get 91.but how? is it guess
  
• 10 years agoHelpfull: Yes(0) No(0)