Yes, an integer can be prime, composite, or neither.
Here's a breakdown:
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Prime Number: A whole number greater than 1 that has only two divisors: 1 and itself. Examples: 2, 3, 5, 7, 11.
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Composite Number: A whole number greater than 1 that has more than two divisors (i.e., it can be divided evenly by numbers other than 1 and itself). Examples: 4, 6, 8, 9, 10.
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Neither: The integer 1 is neither prime nor composite. It only has one divisor, which is itself. The number 0 is also neither prime nor composite. Negative integers are not considered prime or composite.
| Number | Prime? | Composite? | Neither? |
|---|---|---|---|
| 0 | No | No | Yes |
| 1 | No | No | Yes |
| 2 | Yes | No | No |
| 4 | No | Yes | No |
| 6 | No | Yes | No |
| 7 | Yes | No | No |
In summary, every integer is not necessarily either prime or composite. The integer 1 is a notable exception, fitting into neither category.
