To find all the factors of 140, we will follow these steps:
### Step 1: Understand what factors are
Factors of a number are the integers that can be multiplied together to yield that number. For example, if \( a \) and \( b \) are factors of \( n \), then \( a \times b = n \).
### Step 2: Start with the number 1
The first factor of any number is always 1. So, we can start with:
- \( 1 \times 140 = 140 \)
### Step 3: Check for divisibility by 2
Since 140 is an even number, it is divisible by 2:
- \( 2 \times 70 = 140 \)
### Step 4: Check for divisibility by 4
Next, we can check if 4 is a factor:
- \( 4 \times 35 = 140 \)
### Step 5: Check for divisibility by 5
Now, we check for 5:
- \( 5 \times 28 = 140 \)
### Step 6: Check for divisibility by 7
Next, we check for 7:
- \( 7 \times 20 = 140 \)
### Step 7: Check for divisibility by 10
Now, we check for 10:
- \( 10 \times 14 = 140 \)
### Step 8: Check for divisibility by 14
Next, we check for 14:
- \( 14 \times 10 = 140 \) (already counted)
### Step 9: Check for divisibility by 20
Next, we check for 20:
- \( 20 \times 7 = 140 \) (already counted)
### Step 10: Check for divisibility by 28
Next, we check for 28:
- \( 28 \times 5 = 140 \) (already counted)
### Step 11: Check for divisibility by 35
Next, we check for 35:
- \( 35 \times 4 = 140 \) (already counted)
### Step 12: Check for divisibility by 70
Finally, we check for 70:
- \( 70 \times 2 = 140 \) (already counted)
### Step 13: Compile all unique factors
Now we can list all the unique factors we found:
- The factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
### Final Answer
The complete list of factors of 140 is: **1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140.**
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