To find the factors of 154, we will follow these steps:
### Step 1: Understand what factors are
Factors of a number are the integers that can be multiplied together to produce that number. In other words, a factor of 154 is any integer that divides 154 without leaving a remainder.
### Step 2: Start with the smallest factor
The smallest factor of any number is always 1. So, we can say:
- **1 is a factor of 154** (since 154 ÷ 1 = 154).
### Step 3: Check for divisibility by 2
Next, we check if 154 is divisible by 2 (the next smallest integer):
- 154 is even, so it is divisible by 2.
- **2 is a factor of 154** (since 154 ÷ 2 = 77).
### Step 4: Check for divisibility by 3
Now, we check if 154 is divisible by 3:
- The sum of the digits of 154 is 1 + 5 + 4 = 10, which is not divisible by 3.
- Therefore, **3 is not a factor of 154**.
### Step 5: Check for divisibility by 4
Next, we check if 154 is divisible by 4:
- The last two digits of 154 are 54, and 54 is not divisible by 4.
- Therefore, **4 is not a factor of 154**.
### Step 6: Check for divisibility by 5
Next, we check if 154 is divisible by 5:
- Since 154 does not end in 0 or 5, it is not divisible by 5.
- Therefore, **5 is not a factor of 154**.
### Step 7: Check for divisibility by 6
Next, we check if 154 is divisible by 6:
- Since 154 is not divisible by 3, it cannot be divisible by 6.
- Therefore, **6 is not a factor of 154**.
### Step 8: Check for divisibility by 7
Now, we check if 154 is divisible by 7:
- 154 ÷ 7 = 22 (exactly).
- **7 is a factor of 154**.
### Step 9: Check for divisibility by 11
Next, we check if 154 is divisible by 11:
- 154 ÷ 11 = 14 (exactly).
- **11 is a factor of 154**.
### Step 10: Check for divisibility by 14
Since we already found that 11 is a factor, we can check if 14 is a factor:
- 154 ÷ 14 = 11 (exactly).
- **14 is a factor of 154**.
### Step 11: Check for divisibility by 22
Now, we check if 22 is a factor:
- 154 ÷ 22 = 7 (exactly).
- **22 is a factor of 154**.
### Step 12: Check for divisibility by 77
Next, we check if 77 is a factor:
- 154 ÷ 77 = 2 (exactly).
- **77 is a factor of 154**.
### Step 13: Check for divisibility by 154
Finally, we check if 154 is divisible by itself:
- 154 ÷ 154 = 1 (exactly).
- **154 is a factor of 154**.
### Conclusion
The complete list of factors of 154 is:
- **1, 2, 7, 11, 14, 22, 77, and 154**.
