Thread: 4096 has 13 factors WHY

Why is 4096 the smallest number with 13 factors. What does 2^n have to do with it? I understand in order to get an odd number of factors you have to use a perfect square.


Thanks for anything you can add to the picture.

Originally Posted by reagan3nc

Why is 4096 the smallest number with 13 factors. What does 2^n have to do with it? I understand in order to get an odd number of factors you have to use a perfect square.


Thanks for anything you can add to the picture.

this seems like a follow up to this thread. you should have asked this question there

powers of 2 would yield the smallest number. since powers of 1 would only yield 1 and thus would not reach 4096, and powers of 3 (or more, or a product with numbers greater than 2) would be greater than corresponding powers of 2 and so would not be minimum

Hello, reagan3nc!

Why is 4096 the smallest number with 13 factors?
What does 2^n have to do with it?
I understand in order to get an odd number of factors you have to use a perfect square.

There is a theorem that might help explain it.


Given: . . (prime factorization)

. . the number of factors of is: .

. . . . Add one to each exponent and multiply.


Example: .

. . . factors.


We want a number so that: .

Hence, has a prime factorization with an exponent of 12: .

. . And the smallest occurs when


Got it?

Thanks for all your help

Originally Posted by reagan3nc

Why is 4096 the smallest number with 13 factors. What does 2^n have to do with it? I understand in order to get an odd number of factors you have to use a perfect square.


Thanks for anything you can add to the picture.

Since any power of 1 will give only 1 as answer. After this number 2 comes.