sorry the question should be, How many factors of the number 2^5*3^4*5^2 are divisible by 12?

• 48 is answer here is a shortcut write 12 = 2^2 * 3
  we have (2^5 * 3^4 * 5^2) / (2^2 * 3) = 2^3 * 3^3 * 5^2
  
  so to find no. of factors we have formula from theorem of divisibility that is to increase powers by 1 and multiply them
  
  so answer is (3+1)*(3+1)*(2+1) = 48 answer
• 11 years agoHelpfull: Yes(26) No(0)
• vinod...ur answer is wrong.... taking ur first case u didnt count 12 as a factor...moving on....4*9*25 or 4*9*5 ..... dude...u didnt count 4*9 as a factor....??? ...thus ur whole soln is wrong
  
  correct answer::::: 48 if u count x^0 of every number
• 11 years agoHelpfull: Yes(18) No(3)
• 2^5 * 3^4 * 5^2
  ----------------------------------
  2 3 5
  4 9 25
  8 27
  16 81
  32
  
  
  multiplying with different combinations; choosing those with 12 as one of multiplier we have to check each
  for eg: 4*3*5
  4*3*25
  4*9*5
  4*9*25
  4*27*5
  4*27*25
  4*81*5
  4*81*25
  here 8 comb with '4'
  in the same way do for, 8,16,32
  ans
  8+8+8+8=32
  
• 11 years agoHelpfull: Yes(12) No(13)
• 2^5*3^4*5^2 = (2^2*3)*(2^3*3^3*5^2)
  so the factors of 2^3*3^3*5^2 are (3+1)*(3+1)*(2+1) = 48 [power +1 ]
  so total 48 factors
• 11 years agoHelpfull: Yes(5) No(0)
• ans will be 7
  because 2^5*3^4*5^2
  will have (5+1)*(4+1)*(2+1) factors or
  it is equal to=6*5*3=90
  no of factors which r factors of 12 are=90/12=7.5
  so it will be 7
• 11 years agoHelpfull: Yes(4) No(25)
• Sum of all factors
  (2^0+2^1+2^2+2^3+2^4+2^5)(3^0+3^1+3^2+3^3+3^4)(5^0+5^1+5^2)
  No. of factors divisible by 12 means 2^2*3
  In this case we have to take only this factors
  (2^2+2^3+2^4+2^5)(3^1+3^2+3^3+3^4)(5^0+5^1+5^2)
  mean
  4*4*3 =48 factors Answer...
• 11 years agoHelpfull: Yes(4) No(0)
• the number of factors of the given number is (5+1)*(4+1)*(2+1)= 90
  now we will divide the number with 12 i.e 2^2*3^1=2^3*3^3*5^2,,now this immediate result has 48 factors.
  so,the no of factors of the given number are divisible by 12 are (48+1)=49 ans
• 11 years agoHelpfull: Yes(2) No(1)
• @krishanu... do not simply answer anything you like and click on yes... that is a wrong logic...12,24,48,36,60,72,96,108 etc are all factors of the number and are also divisible by 12
• 11 years agoHelpfull: Yes(0) No(6)
• the answer shuld be (48+1)=49....coz we divide the number by 12 i.e 2^2*3
  so we must have to add 1 at the time of result...so the ans will be 49.
• 11 years agoHelpfull: Yes(0) No(3)
• gcrtsedbytg
  
• 10 years agoHelpfull: Yes(0) No(0)