There are exactly 39 composite numbers between 50 and 100.
Understanding Composite Numbers
A composite number is a positive integer that has at least one divisor other than 1 and itself. In other words, it can be formed by multiplying two smaller positive integers. For example, 6 is a composite number because it can be expressed as 2 × 3. Prime numbers, conversely, only have two divisors: 1 and themselves (e.g., 7 is prime). The number 1 is unique and considered neither prime nor composite.
Identifying Composite Numbers Between 50 and 100
To find the composite numbers between 50 and 100, we consider all integers greater than 50 and less than 100. By eliminating the prime numbers in this range, the remaining numbers are composite.
According to a reference from Brainly.in, the composite numbers in this range are:
51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99.
The full list of these 39 composite numbers is presented in the table below:
| Composite Numbers Between 50 and 100 |
|---|
| 51, 52, 54, 55, 56 |
| 57, 58, 60, 62, 63 |
| 64, 65, 66, 68, 69 |
| 70, 72, 74, 75, 76 |
| 77, 78, 80, 81, 82 |
| 84, 85, 86, 87, 88 |
| 90, 91, 92, 93, 94 |
| 95, 96, 98, 99 |
This list confirms that there are indeed a total of 39 composite numbers between 50 and 100. (Source: Brainly.in)
How to Verify the Count
You can verify this count by:
- Counting the total numbers in the range: From 51 to 99, there are 99 - 51 + 1 = 49 numbers.
- Identifying the prime numbers in this range: The prime numbers between 50 and 100 are 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. There are 10 prime numbers.
- Subtracting the primes from the total: Since 1 is not in this range (it's less than 50), all numbers in this range are either prime or composite. Therefore, Total Numbers - Prime Numbers = Composite Numbers: 49 - 10 = 39.
This method further confirms the exact number of composite integers.
