What is the greatest prime you must consider to test whether 868 is prime
2. If two is a factor, then 868 is not prime, and you need test no more.
868=2x2x7x31
In general, to test a number N, the greatest prime you need to try is
√N, since if there is a factor greater than √N, the other factor is less than √N, and you will already have tested that prime.
868
To determine if 868 is a prime number, you need to test its divisibility by prime numbers up to its square root. If a factor is found, then the number is not prime.
In this case, the square root of 868 is approximately 29.45. To check if 868 is divisible by any prime numbers up to 29, you can start dividing it by 2, then 3, then 5, and so on, until you reach the prime numbers up to 29 or find a factor.
Prime numbers up to 29 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
You should test divisibility by these prime numbers to determine if 868 is prime or not.