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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 10^10?

 May 13, 2020
 #1
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20^20 has 861 divisors. 10^10 has 341 divisors. Only 20 multiples of 10^10 are divisors of 20^20 and they are all powers of 2. From 2^1 x 10^10 to 2^20 x 10^10

 

Therefore, the probability is =20 / 861

 May 14, 2020
 #2
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CORRECTION: Sorry, 10^10 has only 121 divisors NOT 341.

 May 14, 2020

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