       Re: All Factors of a number

• To: mathgroup at smc.vnet.net
• Subject: [mg53051] Re: All Factors of a number
• From: Peter Pein <petsie at arcor.de>
• Date: Tue, 21 Dec 2004 05:19:47 -0500 (EST)
• References: <cq6e8m\$2rk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ulrich Sondermann wrote:
> 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}
>

Apply[Times, bt, {2}]
{{1, 2, 3, 5}, {2, 3, 5, 6, 10, 15}, {6, 10, 15, 30}}

is what you want.

Read chapter 2.1.7 in the Mathematica book (Levels in Expressions) - but
it's not easy for beginners.

Peter

--
Peter Pein
Berlin

```

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