       All Factors of a number

• To: mathgroup at smc.vnet.net
• Subject: [mg53025] All Factors of a number
• From: "Ulrich Sondermann" <usondermann at earthlink.net>
• Date: Mon, 20 Dec 2004 06:34:49 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Following is a test code that I am trying to get down to a set of
instructions that will allways put all of the factors of a number in a table
or list.
bt contains all of the factors if I multiply each list entry, however I
cannot accomplish that with a single line, as an example I have broken into
the three lists needed for this example. The results of each "Times@@" is
what I am after all placed into one table. All of my attempts have proved
disasterous, I am new to Mathematica and could do this with nested loops in
any programming language, but this has me stumped.
Thanx!

<<DiscreteMath`Combinatorica`
bt=Table[KSubsets[{1,2,3,5},a],{a,3}]
{{{1},{2},{3},{5}},{{1,2},{1,3},{1,5},{2,3},{2,5},{3,5}},{{1,2,3},{1,2,5},{1
,3,5},{2,3,5}}}
bt1=bt[[1,All]]
{{1},{2},{3},{5}}
Table[Times@@bt1[[a]],{a,4}]
{1,2,3,5}
bt2=bt[[2,All]]
{{1,2},{1,3},{1,5},{2,3},{2,5},{3,5}}
Table[Times@@bt2[[a]],{a,6}]
{2,3,5,6,10,15}
bt3=bt[[3,All]]
{{1,2,3},{1,2,5},{1,3,5},{2,3,5}}
Table[Times@@bt3[[a]],{a,4}]
{6,10,15,30}

```

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