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N-Divisibility (Posted on 2004-02-29) Difficulty: 3 of 5
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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Solution solution | Comment 3 of 4 |

10^40 has 41*41 integers that can divide it, because the integers can be 2^(0 to 40)*5^(0 to 40).  Similarly, 20^30 has 61*31 integers that can divide it.

To get rid of the ones counted twice, I find the GFC of the two, which is 2^40*5^30.  The number of integers that divide this is 41*31.

So the total number of integers that divide at least one is 41*41+61*31-41*31=1681+620=2301

  Posted by Tristan on 2004-02-29 12:18:43
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