Answer:
The greatest prime to consider to test whether 973 is prime is 31. This is because the trial division method, which is the simplest primality test, only requires checking the divisibility of the number by primes up to its square root. The square root of 973 is about 31.2, so we only need to check the primes from 2 to 31. If none of them divides 973 evenly, then 973 is prime. Otherwise, it is composite. I hope this helps you understand how to test for prime numbers.