Math Is Fun Forum

silverpuma

Member

Registered: 2011-06-19

Posts: 80

If you know the sum of the factors of a number, what the number?

back again for help.  A another question from my textbook that although I got the answer right by trying out different numbers but I'm sure there must be a easier/faster, formula way but I can't seem to find it in the previous teaching in the text book.

The question is....The sum of the factors of x is 18.  What is x?

I found the prime factors of 18: they are 2 x 3 x 3  But I could not see how this would help me.  And after a few runs trying different numbers I found that 10 with the factors of 1, 2, 5, 10 added up to 18.  So x = 10  But there has to be a more elegant way than trying numbers until one fits especially if the question was a larger number, for example say..... The sum of the factors of x is 511.  What is x?

That would take a lot of tests before the answer.  Probably the answer is sitting in front of me but.....I think the age is showing:  thanks guys...........

Last edited by silverpuma (2014-03-06 13:35:22)

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“Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.”  ―  Winston Churchill

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: If you know the sum of the factors of a number, what the number?

I got the answer right by trying out different numbers

Wunderbar!

The sum of the factors of x is 511.  What is x?

There are many questions that do not have quick answers and many times a computer must be brought to bear. The answer is 256. For powers of 2 minus one it looks like the answer is predictable with math.

But what if you had said x = 19287152736541109, that ain't so easy at all.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

silverpuma

Member

Registered: 2011-06-19

Posts: 80

Re: If you know the sum of the factors of a number, what the number?

Thanks bobbym.  So from what you said, I'm assuming that the textbook authors probably added this question to get the reader (me) to do what I did, and just figure it out with a few trys.  I enjoyed this as it made me stop and try different things albeit to no avail in the end but the ponder was good.  Though on the other hand it did leave me a bit perturbed as it looked to begin with a fairly straight forward question that after a bit of thinking through I thought I will be able to come up with a formula or number of steps to answer this question and others like it without the tests I had to do.  More of a definitive method.

I had thought I must be missing something easy since I expected the summary questions at the end of the chapter (where this question was) would have been of the type covered and explained with solutions in the pages I had finished studying.  So I quickly scanned the previous dozen pages but I still couldn't find any clarity.  It makes me aware that these type of questions might be lurking for me as I progress further....yum yum:)

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“Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.”  ―  Winston Churchill

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: If you know the sum of the factors of a number, what the number?

Hi;

If they pick numbers that are powers of 2 minus 1 as 511 is or 1023 or 2047 then the question is easy to answer.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.