need to know a number that has exactly 11 factors??  TOPIC_SOLVED

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need to know a number that has exactly 11 factors??

Postby babyZ on Sun Mar 29, 2009 5:59 pm

we got this math project called 'Numbers with a fixed number of factors.' we need to know a number that has exactly 11 factors!! we keep trying, but we think maybe this might be a trick question and there is no number with exactly 11 factors. Please help!
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Postby stapel_eliz on Sun Mar 29, 2009 7:44 pm

Try looking at a few numbers, finding all of their factors, and seeing what patterns you can find.

For instance, the number 8 has factor pairs of 1 and 8, and 2 and 4. This is four factors.

The number 9 has factor pairs of 1 and 9, and 3 and 3. Since "3" is listed twice, this is actually only three factors.

The number 10 has factor pairs of 1 and 10, and 2 and 5: four factors.

The number 11, being prime, has only the pair 1 and 11: two factors. (So any prime will have just the two factors, and now you know not to bother with primes.)

The number 12 has factor pairs 1 and 12, 2 and 6, and 3 and 4: six factors.

The number 16 has factor pairs 1 and 16, 2 and 8, and 4 and 4. Since "4" is occurs twice, this is actually only five factors.

Notice that we always had an even number of factors, unless the number was a square, so that one of the pairs was actually the same factor twice. What does this suggest...? :wink:
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Re: need to know a number that has exactly 11 factors??  TOPIC_SOLVED

Postby babyZ on Sun Mar 29, 2009 11:51 pm

we tryed squares
squares of primes didnt give enough
we finally found 1024:

1&1024, 2&512, 4&256, 8&128, 16&64, 32&32
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Re: need to know a number that has exactly 11 factors??

Postby sparkle2009 on Thu Apr 02, 2009 12:22 pm

Take any 11 primes at random and multiply them to get your desired number
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Postby stapel_eliz on Thu Apr 02, 2009 10:37 pm

sparkle2009 wrote:Take any 11 primes at random and multiply them to get your desired number

Actually, no. For instance, the product of 3 and 5, both numbers being prime, is 15, and 15 has factors 1, 3, 5, and 15.

:oops:
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