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We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 10^{20}? Express your answer as a fraction in simplest form.

 Sep 1, 2021
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[20^20] / [10^20] ==1,048,576 ==2^20 ==which has 20 + 1 ==21 divisors.

 

20^20 ==1.048576e+26 = 2^40 * 5^20 ==41 * 21 ==861 divisors.

 

The probability is: 21 / 861 == 1 / 41

 Sep 1, 2021

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