The prime factorization of N is 3^3 * 7^r. If N has exactly 16 positive integer factors, what is the value of R?

13

Step-by-step explanation:

N = 3^3 * 7^r

N has 16 integer factors

3^3 is 3 factors

That means 7^r must be 16-3 or 13 factor

7^r must be 13 terms

so 7^r must be 7*7*7 ... * 7 so that there are 13 term which means

r must be 13

3^3 * 7^r has (3 + 1) * (r + 1) = 16 factors.

So r must be 3.