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 N-Divisibility (Posted on 2004-02-29)
How many positive integers divide at least one of 10^40 and 20^30?

 See The Solution Submitted by DJ Rating: 4.1111 (9 votes)

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 Puzzle Solution With Explanation Comment 4 of 4 |

Let D(x) denote the total number of divisors of x, including 1 and itself.

Thus, taking m = 10^40 = (5^40)*(2^40), and:
n = 20^30 = (2^60)*(5^30), we have:

p = GCD(m, n) = (2^40)*(5^30)

Thus, the required number of divisors (v) dividing at least one of 10^40 and 20^30 is given by:

V = D(m)+ D(n) - D(p)
= 41^2 + 61*31 - 41*31
= 2301

 Posted by K Sengupta on 2007-05-28 11:55:32
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