The prime numbers between 0 and 10 are 2, 3, 5, and 7.
Identifying Prime Numbers
To determine the prime numbers within a specific range, such as between 0 and 10, it's essential to understand what defines a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Understanding Prime Numbers
Let's break down the definition and apply it to the numbers from 0 to 10:
- Numbers less than or equal to 1 are not considered prime numbers by definition. This includes 0 and 1.
- Composite numbers are natural numbers greater than 1 that are not prime, meaning they have more than two distinct positive divisors (including 1 and themselves).
Numbers Between 0 and 10
Here's an analysis of each whole number between 0 and 10:
| Number | Divisors | Prime? | Reasoning |
|---|---|---|---|
| 0 | All | No | Not a natural number greater than 1. |
| 1 | 1 | No | By definition, prime numbers must be greater than 1. |
| 2 | 1, 2 | Yes | It is the smallest and only even prime number. |
| 3 | 1, 3 | Yes | Only divisible by 1 and itself. |
| 4 | 1, 2, 4 | No | Divisible by 2 (in addition to 1 and 4). |
| 5 | 1, 5 | Yes | Only divisible by 1 and itself. |
| 6 | 1, 2, 3, 6 | No | Divisible by 2 and 3. |
| 7 | 1, 7 | Yes | Only divisible by 1 and itself. |
| 8 | 1, 2, 4, 8 | No | Divisible by 2 and 4. |
| 9 | 1, 3, 9 | No | Divisible by 3. |
| 10 | 1, 2, 5, 10 | No | Divisible by 2 and 5. |
Reference Information on Prime Numbers
The list provided by Third Space Learning confirms these findings. According to their article, "What Is A Prime Number? Explained for Parents, Teachers & Children" on thirdspacelearning.com, "The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29."
From this authoritative list, we can directly see that the prime numbers which fall within the range of 0 to 10 are indeed 2, 3, 5, and 7. The reference also highlights that prime numbers extend well beyond this initial range, with 25 prime numbers between 1 and 100, and examples of very large prime numbers like 21,577.
Conclusion
Based on the definition of a prime number and verification with reliable sources, the exact answer to the question is that the prime numbers between 0 and 10 are 2, 3, 5, and 7.
