Math Community Quiz

[Runer112]

I haven't actually figured this out yet myself, but it sounds like an interesting challenge, so:

Find the smallest positive integer that has at least 5 factors (including 1 and itself) for which the number of 1s in its base 2 representation equals the number of factors.

I hope this doesn't end up being too ridiculous to figure out.


EDIT: Reduced the minimum number of factors to 5.

[ruler501]

My calculator said nine I'll have to check that. How did you get your answer I just tried to make it more accurate at each decimal place

Runner did you mean have the ones in its binary form when added together equal the number of factors? Are you talking about prime factors?

Do they need to be seperate prime factors? if not it would be 125 or 1101111 factors are 125*1, 5*25, 5*5

Edit: Never Mind I'm temporarily stupid

[Runer112]

Runner did you mean have the ones in its binary form when added together equal the number of factors?

Yes. By the way, is it ok that I changed the question slightly to reduce the minimum number of factors? Because now that I looked at it 6 is actually too easy

[nemo]

64?

edit: sorry i just made a program to figure it out and realized this makes no sense. disregard.

nevermind, it was a bug in the program. 63!

[Runer112]

Yeah, 63 is it. I probably should've thought a bit more before picking a question with, once you see it, such an obvious answer.

[jnesselr]

126 actually. 63 only has 5 factors including itself.

[Runer112]

What? I counted 1, 3, 7, 9, 21, and 63.

[nemo]

Yeah, 63 is it. I probably should've thought a bit more before picking a question with, once you see it, such an obvious answer.

yeah, but it seemed tricky. it was a cool problem. i'll think about what my question will be...

[jnesselr]

What? I counted 1, 3, 7, 9, 21, and 63.

Okay, wait, then you have to define factors here. 3*3*7=63. So I thought you meant that kind of factor.  And you just reduced it to 5, too.  By my definition:

3=7
4=15
5=110
6=126
7=720
8=1215
9=8019
10=10206

So since I was confused, who gets it? I thought factors as in it's prime factorization.

[ruler501]

Very Interesting problem wish I had thought it through more/seen your edit about 5 factors instead of 6 and I had been working with prime factors

[Runer112]

Well it turns out the answer had 6 factors anyways

[jnesselr]

Well it turns out the answer had 6 factors anyways

So who wins? and 6 prime factors or what?

[Runer112]

I didn't specify that the factors had to be prime (didn't intend to specify it either, but I understand the confusion) so nemo got it.

[jnesselr]

I didn't specify that the factors had to be prime (didn't intend to imply that, but I understand the confusion) so nemo got it.

Okay. From now on, I think we need to specify random stuff.  For example:

No, that balloon isn't traveling the speed of light, but e^9.25 under it.

[ruler501]

I think Nemo should get it. He got the correct answer first