To find all the factors of 72, we can 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: Start with the Number 1
The first factor of any number is always 1. Since \( 1 \times 72 = 72 \), we have our first pair of factors: \( (1, 72) \).
**Hint:** Always start with 1 and the number itself as the first pair of factors.
### Step 3: Check for Other Factors
Next, we will check for other integers that can divide 72 without leaving a remainder. We can do this by testing integers from 1 up to the square root of 72 (approximately 8.49).
- **2:** \( 72 \div 2 = 36 \) → Pair: \( (2, 36) \)
- **3:** \( 72 \div 3 = 24 \) → Pair: \( (3, 24) \)
- **4:** \( 72 \div 4 = 18 \) → Pair: \( (4, 18) \)
- **6:** \( 72 \div 6 = 12 \) → Pair: \( (6, 12) \)
- **8:** \( 72 \div 8 = 9 \) → Pair: \( (8, 9) \)
**Hint:** Continue testing integers until you reach the square root of the number.
### Step 4: List All Unique Factors
Now, we compile all the unique factors we found:
- From the pairs: \( 1, 72, 2, 36, 3, 24, 4, 18, 6, 12, 8, 9 \)
### Step 5: Write the Final List of Factors
The complete list of factors of 72 is:
\[ 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 \]
**Hint:** Make sure to include all unique factors and avoid duplicates.
### Conclusion
The factors of 72 are \( 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, \) and \( 72 \).
