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N-Divisibility II (Posted on 2011-12-17) Difficulty: 3 of 5
Consider four base ten positive integers 4298, 7070, 10542 and 15428 and, determine the total number of positive integers dividing:

(I) At least one of the four given numbers.

(II) At least two of the four given numbers.

(III) At least three of the four given numbers.

(IV) Each of the four given numbers.

No Solution Yet Submitted by K Sengupta    
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Last things first (partial spoiler) | Comment 1 of 5
The four numbers are (2*3*7)^98, (2*5*7)^70, (3*5*7)^42, and (2*7*11)^28.

Part (IV) -- Any number which divides all four must divide 7^28
There are 29 in total

Edited on December 17, 2011, 12:20 pm
  Posted by Steve Herman on 2011-12-17 12:10:55

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