Maths-
General
Easy

Question

Number of positive integers that are divisors of atleast one of the numbers 10 to the power of 10 end exponent semicolon 15 to the power of 7 end exponent semicolon 18 to the power of 11 end exponentis

  1. 461    
  2. 436    
  3. 435    
  4. 434    

The correct answer is: 435


    Number of divisors of10 to the power of 10 end exponent equals 2 to the power of 10 end exponent times 5 to the power of 10 end exponent rightwards arrow 11 cross times 11 equals 121.(1)
    ly Number of divisors of15 to the power of 7 end exponent equals 3 to the power of 7 end exponent.5 to the power of 7 end exponent rightwards arrow 8 cross times 8 equals 64...(2)
    And Number of divisors of8 to the power of 11 end exponent equals 2 to the power of 11 end exponent times 3 to the power of 22 end exponent rightwards arrow 12 cross times 23 equals 276...(3)
    Common in (1) and (2) = 8 (because of the presence of in both)
    Common in (2) and (3) = 8 (because of the presence of in both)
    Common in (3) and (1) = 11 (because of the presence of in both)
    However we have not counted the factor which divide all the three number i.e. 1
    Hence final answer = 121 plus 64 plus 276 minus left parenthesis 8 plus 8 plus 11 right parenthesis plus 1 equals 435

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