Find all the factors of 105.

Answer

To find all the factors of 105, we will follow these steps:

### Step 1: Understand the Definition of Factors
Factors of a number are integers that can be multiplied together to produce that number. For example, if \( a \) and \( b \) are factors of \( n \), then \( a \times b = n \).

**Hint:** Remember that factors come in pairs that multiply to give the original number.

### Step 2: Check for Divisibility
To find the factors of 105, we will check which numbers divide 105 without leaving a remainder. We will start from 1 and go up to 105.

**Hint:** Start with the smallest integers and work your way up.

### Step 3: List the Factors
1. **1**: \( 1 \times 105 = 105 \)
2. **2**: 105 is odd, so it is not divisible by 2.
3. **3**: \( 3 \times 35 = 105 \)
4. **4**: 105 is not divisible by 4.
5. **5**: \( 5 \times 21 = 105 \)
6. **6**: 105 is not divisible by 6.
7. **7**: \( 7 \times 15 = 105 \)
8. **8**: 105 is not divisible by 8.
9. **9**: 105 is not divisible by 9.
10. **10**: 105 is not divisible by 10.
11. **11**: 105 is not divisible by 11.
12. **12**: 105 is not divisible by 12.
13. **13**: 105 is not divisible by 13.
14. **14**: 105 is not divisible by 14.
15. **15**: \( 15 \times 7 = 105 \)
16. **21**: \( 21 \times 5 = 105 \)
17. **35**: \( 35 \times 3 = 105 \)
18. **105**: \( 105 \times 1 = 105 \)

### Step 4: Compile the List of Factors
From our checks, the factors of 105 are:
- 1
- 3
- 5
- 7
- 15
- 21
- 35
- 105

### Final Answer
The complete list of factors of 105 is: **1, 3, 5, 7, 15, 21, 35, and 105.**

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