The number of composite numbers between 101 and 120 is :

Options

A. 11
B. 12
C. 13
D. 14

Answer

To find the number of composite numbers between 101 and 120, we can follow these steps:

### Step 1: Understand Composite Numbers
Composite numbers are positive integers that have more than two distinct positive divisors (factors). This means they can be formed by multiplying two smaller positive integers.

### Step 2: Identify the Range
We need to find composite numbers in the range from 101 to 120. This means we will consider the numbers 102, 103, ..., 119, and 120.

### Step 3: List the Numbers
The numbers between 101 and 120 are:
- 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

### Step 4: Identify Composite Numbers
Now, we will identify which of these numbers are composite:
- **102**: Composite (2 x 51)
- **103**: Prime
- **104**: Composite (2 x 52)
- **105**: Composite (3 x 35)
- **106**: Composite (2 x 53)
- **107**: Prime
- **108**: Composite (2 x 54)
- **109**: Prime
- **110**: Composite (2 x 55)
- **111**: Composite (3 x 37)
- **112**: Composite (2 x 56)
- **113**: Prime
- **114**: Composite (2 x 57)
- **115**: Composite (5 x 23)
- **116**: Composite (2 x 58)
- **117**: Composite (3 x 39)
- **118**: Composite (2 x 59)
- **119**: Composite (7 x 17)
- **120**: Composite (2 x 60)

### Step 5: Count the Composite Numbers
From the list, the composite numbers are:
- 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120

Counting these gives us:
1. 102
2. 104
3. 105
4. 106
5. 108
6. 110
7. 111
8. 112
9. 114
10. 115
11. 116
12. 117
13. 118
14. 119
15. 120

### Conclusion
There are **15 composite numbers** between 101 and 120.