Rabbitaoy wrote:for example 6 has four factors 1, 2, 3, and 6. what about 6 to the 6th power?

Welcome to BTG!!!!

6^6
= (2 * 3) ^ 6
= 2^6 * 3^6

So total number of factors = (6+1)*(6+1) = 49

This is a formula: first break the number to all possible prime numbers (along with the powers) Then add one to each power and multiple.

N = a^x*b^y*c^z where a b c are distinct prime numbers and x y and z are corresponding powers then
Total number of factors = (x+1)*(y+1)*(z+1)

Try the same for 36 = 2^2 * 3^2
Total factors = (2+1)*(2+1) = 9 which are [1,2,3,4,6,9,12,18,36]

Thanks Shovan.

What about a single prime number with a power attached to it? say 3^27? Can I say it has 27+1=28 number of factors?

Rabbitaoy wrote:Thanks Shovan.

What about a single prime number with a power attached to it? say 3^27? Can I say it has 27+1=28 number of factors?

Yes