A prime number is a whole number greater than 1 that has only two distinct positive divisors: 1 and itself. A composite number is a whole number greater than 1 that has more than two distinct positive divisors (i.e., it can be divided evenly by numbers other than 1 and itself).
Prime Numbers Explained
- Definition: A number is prime if it's only divisible by 1 and itself.
- Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 are all prime numbers.
- Characteristics:
- The number 1 is not considered a prime number.
- 2 is the only even prime number. All other even numbers are divisible by 2 and therefore have more than two factors.
- Prime numbers are the "building blocks" of all other whole numbers because any whole number can be expressed as a product of prime numbers (this is called prime factorization).
Composite Numbers Explained
- Definition: A number is composite if it has divisors other than 1 and itself. In other words, it can be evenly divided by at least one other number.
- Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 are all composite numbers.
- Characteristics:
- All even numbers greater than 2 are composite.
- Any number ending in 0 or 5 (except for 5 itself) is composite because it's divisible by 5.
Comparison Table
| Feature | Prime Number | Composite Number |
|---|---|---|
| Number of Factors | Exactly 2 (1 and itself) | More than 2 |
| Divisibility | Only divisible by 1 and itself | Divisible by 1, itself, and at least one other number |
| Examples | 2, 3, 5, 7, 11, 13 | 4, 6, 8, 9, 10, 12 |
| Status of 1 | Neither prime nor composite | Neither prime nor composite |
In summary, prime numbers are the fundamental building blocks of all integers, while composite numbers are those that can be broken down further into smaller factors.
