Wikipedia:Reference desk/Archives/Mathematics/2009 June 28

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June 28

Divisible by 126

What numbers are divisable by 126? Thanks --WontYouPoloMarco (talk) 17:59, 28 June 2009 (UTC)

There's not really any answer much better than 'those which are divisible by 126'. You can rephrase that as 'those n such that there exists m such that n=126m' but that's hardly an improvement. What sort of answer did you have in mind? Algebraist 18:06, 28 June 2009 (UTC)

0 126 252 378 504 630 756 882 1008 1134 1260 1386 1512 1638 1764 1890 2016 2142 2268 2394 and so on. Also their negatives. Bo Jacoby (talk) 18:48, 28 June 2009 (UTC).

Multiples of 126? --84.221.69.148 (talk) 19:19, 28 June 2009 (UTC)

The OP probably has Divisibility rules in mind. Since $126=2\cdot 3^{2}\cdot 7$, you need to verify that the number is divisible by 2, 9 and 7. For that you can use the rules in the linked article. -- Meni Rosenfeld (talk) 20:02, 28 June 2009 (UTC)

Meni Rosenfeld's answer is too complicated. One need not go into prime factorizations. Here's the answer:

 0 × 126,

±1 × 126,

±2 × 126,

±3 × 126,

±4 × 126,

±5 × 126,

±6 × 126,

.....

Michael Hardy (talk) 22:55, 28 June 2009 (UTC)

Meni's answer provides an efficient procedure for deciding if any arbitrary number, given in base 10, is divisible by 126. Sure, it's 'complicated', but that could be exactly what the OP needs (assuming the OP wasn't just doodling on the internet). --COVIZAPIBETEFOKY (talk) 00:38, 29 June 2009 (UTC)

I have just enough faith in humanity to assume that the OP was not looking for a list of numbers divisible by 126. That means he was looking for something else. Both divisibility rules and factors are good guesses, and being "complicated" is meaningless if that is the simplest way to answer what the OP meant to ask. -- Meni Rosenfeld (talk) 11:48, 29 June 2009 (UTC)

The OP didn't ask for an algorithm for ascertaining divisibility by 126; but rather: which numbers are divisible by 126? It is altogether possible that that was the intended meaning of the question. Michael Hardy (talk) 01:08, 30 June 2009 (UTC)

Just in case the question was supposed to be "What numbers is 126 divisible by?" and it got mangled, the answer would be:

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.

Michael Hardy (talk) 23:00, 28 June 2009 (UTC)

calculate pi with hot dogs

How does this work? Mac Davis (talk) 19:49, 28 June 2009 (UTC)

See Buffon's needle. -- Meni Rosenfeld (talk) 19:56, 28 June 2009 (UTC)

And Buffon's noodle, for another gastronomic version. --84.221.69.148 (talk) 05:24, 29 June 2009 (UTC)