The exact answer is 6.
Understanding composite numbers between 21 and 30 involves identifying the integers within this range and determining which ones are composite. A composite number is a positive integer that can be formed by multiplying two smaller positive integers. In other words, it's a number that has at least one divisor other than 1 and itself. Prime numbers, in contrast, have exactly two distinct positive divisors: 1 and themselves. The number 1 is neither prime nor composite.
Identifying Composite Numbers
The range "between 21 and 30" typically refers to the integers greater than 21 and less than 30. These numbers are:
22, 23, 24, 25, 26, 27, 28, 29
We need to examine each number in this list to see if it's composite. We can do this by checking for divisors other than 1 and the number itself.
- 22: Divisible by 2 and 11 (2 x 11 = 22). Composite.
- 23: Only divisible by 1 and 23. Prime.
- 24: Divisible by 2, 3, 4, 6, 8, 12. Composite.
- 25: Divisible by 5 (5 x 5 = 25). Composite.
- 26: Divisible by 2 and 13 (2 x 13 = 26). Composite.
- 27: Divisible by 3 and 9 (3 x 9 = 27). Composite.
- 28: Divisible by 2, 4, 7, 14. Composite.
- 29: Only divisible by 1 and 29. Prime.
Based on this analysis, the composite numbers between 21 and 30 are 22, 24, 25, 26, 27, and 28.
Reference Confirmation
According to the reference from homework.study.com, the composite numbers between 20 and 30 are: 20, 21, 22, 24, 25, 26, 27, 28, and 30.
Let's look at this list and select only the numbers that are strictly greater than 21 and strictly less than 30:
- 20 - Not between 21 and 30
- 21 - Not between 21 and 30
- 22 - Between 21 and 30
- 24 - Between 21 and 30
- 25 - Between 21 and 30
- 26 - Between 21 and 30
- 27 - Between 21 and 30
- 28 - Between 21 and 30
- 30 - Not between 21 and 30
The composite numbers from the reference list that fall between 21 and 30 are indeed 22, 24, 25, 26, 27, and 28.
Summary of Composite Numbers
Here's a breakdown of the numbers in the range and their classification:
| Number | Classification | Reason |
|---|---|---|
| 22 | Composite | Has factors other than 1 and 22 (e.g., 2) |
| 23 | Prime | Only factors are 1 and 23 |
| 24 | Composite | Has factors other than 1 and 24 (e.g., 2) |
| 25 | Composite | Has factors other than 1 and 25 (e.g., 5) |
| 26 | Composite | Has factors other than 1 and 26 (e.g., 2) |
| 27 | Composite | Has factors other than 1 and 27 (e.g., 3) |
| 28 | Composite | Has factors other than 1 and 28 (e.g., 2) |
| 29 | Prime | Only factors are 1 and 29 |
The composite numbers between 21 and 30 are:
- 22
- 24
- 25
- 26
- 27
- 28
Counting these numbers, we find there are 6 composite numbers in this range.
