How many composite numbers are in between 50 and 100 (inclusive of 50 and 100)?

Options

A. 39
B. 40
C. 41
D. 42

Explanation

To find how many composite numbers are between 50 and 100 (inclusive), we will follow these steps:

### Step 1: Understand Composite Numbers
Composite numbers are natural numbers greater than 1 that are not prime, meaning they have more than two distinct positive divisors (1 and the number itself).

### Step 2: List the Numbers from 50 to 100
We will list all the numbers from 50 to 100:
- 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

### Step 3: Identify Composite Numbers
Now, we will identify which of these numbers are composite. We can do this by checking each number to see if it has more than two factors.

- **Composite Numbers**:
- 50 (1, 2, 5, 10, 25, 50)
- 51 (1, 3, 17, 51)
- 52 (1, 2, 4, 13, 26, 52)
- 54 (1, 2, 3, 6, 9, 18, 27, 54)
- 55 (1, 5, 11, 55)
- 56 (1, 2, 4, 7, 8, 14, 28, 56)
- 57 (1, 3, 19, 57)
- 58 (1, 2, 29, 58)
- 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
- 62 (1, 2, 31, 62)
- 63 (1, 3, 7, 9, 21, 63)
- 64 (1, 2, 4, 8, 16, 32, 64)
- 65 (1, 5, 13, 65)
- 66 (1, 2, 3, 6, 11, 22, 33, 66)
- 68 (1, 2, 4, 17, 34, 68)
- 69 (1, 3, 23, 69)
- 70 (1, 2, 5, 7, 10, 14, 35, 70)
- 72 (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72)
- 74 (1, 2, 37, 74)
- 75 (1, 3, 5, 15, 25, 75)
- 76 (1, 2, 4, 19, 38, 76)
- 77 (1, 7, 11, 77)
- 78 (1, 2, 3, 6, 13, 26, 39, 78)
- 80 (1, 2, 4, 5, 8, 10, 16, 20, 40, 80)
- 81 (1, 3, 9, 27, 81)
- 82 (1, 2, 41, 82)
- 84 (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84)
- 85 (1, 5, 17, 85)
- 86 (1, 2, 43, 86)
- 87 (1, 3, 29, 87)
- 88 (1, 2, 4, 8, 11, 22, 44, 88)
- 90 (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90)
- 91 (1, 7, 13, 91)
- 92 (1, 2, 4, 23, 46, 92)
- 93 (1, 3, 31, 93)
- 94 (1, 2, 47, 94)
- 95 (1, 5, 19, 95)
- 96 (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96)
- 98 (1, 2, 7, 14, 49, 98)
- 99 (1, 3, 9, 11, 33, 99)
- 100 (1, 2, 4, 5, 10, 20, 25, 50, 100)

### Step 4: Count the Composite Numbers
Now we will count the composite numbers identified:
- Composite numbers between 50 and 100 are: 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 92, 94, 96, 98, 99, 100.

### Total Count
The total number of composite numbers between 50 and 100 is **36**.