Explanation;
A prime number is a positive integer that has exactly two positive integer factors, 1 and itself.
Note that the definition of a prime number doesn't allow 1 to be a prime number:
1 only has one factor, namely 1.
Prime numbers have exactly two factors, not "at most two" or anything like that. When a number has more than two factors it is called a composite number.
Prime Numbers between 1 and 200 are;
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199}
So the above listed examples are prime numbers because they have only two factors.