Write all the factors of
54

Answer

To find all the factors of 54, 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. For example, if we have a number \( n \), then \( a \) is a factor of \( n \) if \( n \div a \) results in an integer.

### Step 2: Start with the smallest factor
The smallest factor of any number is always 1. So, we start with:
- **Factor**: 1

### Step 3: Check for divisibility by 2
Next, we check if 54 is divisible by 2. Since 54 is an even number:
- **Factor**: 2 (because \( 54 \div 2 = 27 \))

### Step 4: Check for divisibility by 3
Now, we check if 54 is divisible by 3. We can do this by adding the digits of 54 (5 + 4 = 9), and since 9 is divisible by 3:
- **Factor**: 3 (because \( 54 \div 3 = 18 \))

### Step 5: Check for divisibility by 4
Next, we check if 54 is divisible by 4. Since \( 54 \div 4 = 13.5 \) (not an integer), 4 is not a factor:
- **Not a Factor**: 4

### Step 6: Check for divisibility by 5
Next, we check if 54 is divisible by 5. Since 54 does not end in 0 or 5, it is not divisible by 5:
- **Not a Factor**: 5

### Step 7: Check for divisibility by 6
Now, we check if 54 is divisible by 6. Since \( 54 \div 6 = 9 \):
- **Factor**: 6

### Step 8: Check for divisibility by 7
Next, we check if 54 is divisible by 7. Since \( 54 \div 7 \) is not an integer:
- **Not a Factor**: 7

### Step 9: Check for divisibility by 8
Next, we check if 54 is divisible by 8. Since \( 54 \div 8 = 6.75 \) (not an integer), 8 is not a factor:
- **Not a Factor**: 8

### Step 10: Check for divisibility by 9
Now, we check if 54 is divisible by 9. Since \( 54 \div 9 = 6 \):
- **Factor**: 9

### Step 11: Check for divisibility by 10
Next, we check if 54 is divisible by 10. Since 54 does not end in 0, it is not divisible by 10:
- **Not a Factor**: 10

### Step 12: Check for divisibility by 11
Next, we check if 54 is divisible by 11. Since \( 54 \div 11 \) is not an integer:
- **Not a Factor**: 11

### Step 13: Check for divisibility by 12
Next, we check if 54 is divisible by 12. Since \( 54 \div 12 = 4.5 \) (not an integer), 12 is not a factor:
- **Not a Factor**: 12

### Step 14: Check for divisibility by 13, 14, etc.
Continuing this process, we find that 54 is not divisible by 13, 14, etc., until we reach 54 itself:
- **Factor**: 54 (since \( 54 \div 54 = 1 \))

### Step 15: Compile all factors
Now, we can compile all the factors we found:
- **Factors of 54**: 1, 2, 3, 6, 9, 18, 27, 54

### Final Answer:
The complete list of factors of 54 is: **1, 2, 3, 6, 9, 18, 27, 54**

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