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# factors

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what is the smallest number with 13 factors?

Guest Jan 24, 2016

#4
+5

{nl} Hmmmm...my first answer was not correct.   But what about 4000 ?

1  2  4  5  8  10 20 40 50 100 200 400 500 1000 4000     has 15 !    and it's smaller than 4096

2000

1 2 4 5 10 20 50 100 200 400 500 1000 4000       13 !   and smaller than 4096

1500

1 2 3 5 10 20 50 75 100 300 500 750 1500    13   ! and smaller still

1200

1 2 3 4 5 6 10 12 20 50 100 150 200 300 400 600 1200      17 !   and smaller still

There may be smaller still......

900

1 2 3 4 5 6 10 20 30 50 60 100 150 300 900    15 !

600

1 2 3 4 5 6 10 20 30 50 75 100 200 300 600    15 !

300

1 2 3 4 5 6 10 15 20 50 60 75 100 300     14 !

240

1 2 3 4 5 6 8 10 12 20 30 40 80 120 240    15!

Maybe 240??

120

1 2 3 4 5 6 8 10 12 15 20 30 40 60 120

Guest Jan 24, 2016
edited by Guest  Jan 24, 2016
Sort:

#1
+5

what is the smallest number with 13 factors?

Guest Jan 24, 2016
#2
+5

Hard to say....if you are talking about WHOLE numbers AND you can use them more than once

then   1^13  = 13

If you cannot use the same factor twice then 13! would be an answer

(13x12x11x10x19x8x7x6x5x4x3x2x1)

If you can use NEGATIVES then SMALLEST number takes on a whole new meaning as any negative is smaller than any positive number...

Guest Jan 24, 2016
#3
+5210
+5

2^12 = 4,096

So you have 13 factors, one of the factors is 1, so take that out. Then give 2 the power of 12 to find the number.

The factors are:1,2,4,8,16,32,64,128,256,512,1024,2048,4096

rarinstraw1195  Jan 24, 2016
#4
+5

{nl} Hmmmm...my first answer was not correct.   But what about 4000 ?

1  2  4  5  8  10 20 40 50 100 200 400 500 1000 4000     has 15 !    and it's smaller than 4096

2000

1 2 4 5 10 20 50 100 200 400 500 1000 4000       13 !   and smaller than 4096

1500

1 2 3 5 10 20 50 75 100 300 500 750 1500    13   ! and smaller still

1200

1 2 3 4 5 6 10 12 20 50 100 150 200 300 400 600 1200      17 !   and smaller still

There may be smaller still......

900

1 2 3 4 5 6 10 20 30 50 60 100 150 300 900    15 !

600

1 2 3 4 5 6 10 20 30 50 75 100 200 300 600    15 !

300

1 2 3 4 5 6 10 15 20 50 60 75 100 300     14 !

240

1 2 3 4 5 6 8 10 12 20 30 40 80 120 240    15!

Maybe 240??

120

1 2 3 4 5 6 8 10 12 15 20 30 40 60 120

Guest Jan 24, 2016
edited by Guest  Jan 24, 2016
#5
+91779
+5

what is the smallest number with 13 factors?

Mmm, it does not say prime factors

1,2,3,4,6,8,9,12,16,18,24,27,32     that 13

2^5* 3^3 = 864

I think 864 has 13 factors but it might not be the smallest.

1,2,3,4,5,6,8,9,10,12,15,16, 18

1*2*2*2*2 * 3*3* 5 =  16*9*5 = 720

I think that 720 has 13 factors

1,2,4,8,16,32,64,128,256,......2^12

2^12 = 4096

Mmm

Ok I am guessing at 720   :)

Can you find a smaller number with 13 factors?

Melody  Jan 25, 2016
#6
+91779
0

I see guest says it is 120....

120=2*60

=2*2*2*30

=2*2*2*2*15

=2*2*2*2*3*5

factors

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120   I get 16 factors.....are some of them wrong.

Mmm i guess my logic was up the  creek.  I now think the answer must be less than 120 ....

Thanks Guest.

Melody  Jan 25, 2016

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