1. The number 47 is prime. The only factors are 1 and itself. We can check by dividing 47 over the list of primes smaller than 47. To be more efficient, we can stop once we reach sqrt(47) = 6.85. So we only need to check the primes {2, 3, 5} to show they are not factors of 47 to show that 47 is prime.
=====================================
2. The number 81 is composite. It is not prime because it has factors other than 1 and itself.
There are 5 factors and they are
1, 3, 9, 27, 81
Note how each factor listed is a power of 3 (1 = 3^0, 3 = 3^1, 9 = 3^2, 27 = 3^3, 81 = 3^4)
The prime factorization of 81 is
81 = 3*3*3*3 = 3^4
