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I thought that numbers were coprime if the only positive integer that evenly divides all of them is 1.

However Wolfram Alpha say that 6, 10 and 15 are not coprime. But the only number that divides all of these is 1?

Are a list of numbers coprime if ALL pairs of numbers are coprime?

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wolframalpha.com/input/?i=are+6%2C+10+and+15+coprime%3F –  user26069 Apr 26 '12 at 12:36
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@user26069, CoprimeQ checks for pairwise coprimality. –  lhf Apr 26 '12 at 13:04

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up vote 2 down vote accepted

I can't speak for wolfram, but the standard convention is the one you give: a coprime list of numbers is one in which there is no non-unit that divides all of them. That makes 6, 10, 15 a coprime list.

The stronger concept, where one insists that each pair be coprime, is referred to as "pairwise coprime." The numbers 6, 10, 15 are not pairwise coprime.

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Oh so wolfram should have said; 'not pairwise coprime'. How confusing.. –  user26069 Apr 26 '12 at 12:57

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