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?

CalculatorUser May 31, 2019