+2862 In terms of N, a natural number, how many more positive integral factors does \(24^n\) than \(16^n \)?
What I did:
24^n is now 3^n * 2^3n
16^n is now 2^4n
We can find the number of factors in a number by prime factoring it, then taking each prime factor's exponent and adding 1 to it, then mulitply it with the others.
So 24^n has 3n^2+4n+1 factors
And 16^n has 4n+1 factors
This means that there are 3n^2 more factors.
Am i Right?
