If 68 is a prime number, then the only factors it has are 1 and 68. If it has any other factors besides 1 and 68, then it's NOT prime.
Right away, without any higher math, you can look at just the last digit in 68 . The last digit is '8'. That tells you that '68' is an even number, and THAT tells you that '2' must be one of its factors. So '68' is not a prime number.
The factors of 68 are 1, 2, 4, 17, 34, and 68 .
68 has four more factors besides 1 and 68, so it's not a prime number.