No, that's not quite accurate. Prime numbers do have divisors. The defining characteristic of a prime number is that it has exactly two distinct positive divisors: 1 and itself.
Here's a breakdown:
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Definition of a Prime Number: A prime number is a natural number greater than 1 that has only two positive integer divisors: 1 and the number itself.
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Examples:
- The number 7 is prime because its only divisors are 1 and 7.
- The number 11 is prime because its only divisors are 1 and 11.
- The number 4 is not prime because it has divisors 1, 2, and 4.
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Important Clarification: It's more accurate to say that prime numbers have no divisors other than 1 and themselves. The statement "prime numbers have no divisors" is technically incorrect.
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Composite Numbers: Numbers greater than 1 that have more than two divisors are called composite numbers.
| Number | Divisors | Prime? |
|---|---|---|
| 2 | 1, 2 | Yes |
| 3 | 1, 3 | Yes |
| 4 | 1, 2, 4 | No |
| 5 | 1, 5 | Yes |
| 6 | 1, 2, 3, 6 | No |
In summary, prime numbers are characterized by having exactly two divisors: 1 and themselves. They don't have no divisors; they simply don't have any other divisors beyond these two.
