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Easy

Question

Number of positive integers that are divisiors 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 exponent is

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

The correct answer is: 435


    Number of divisors of 1010 = 210 510 11 11 = 121 ....(1)
    ly Number of divisors of 157 = 37 57 8 8 = 64 ....(2)
    and Number of divisors of 811 = 211 322 12 23 = 276 ....(3)
    common in (1) and (2) = 8 (because of the presence of 5 to the power of 7 end exponent 57 in both)
    common in (2) and (3) = 8 (because of the presence of 3 to the power of 7 end exponent in both)
    common in (3) and (1) = 11 (because of the presence of 2in both)
    However we have not counted the factor which divide all the three number i.e. 1
    hence final answer = 121 + 64 + 276 - (8 + 8 + 11) + 1 = 435

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