To find the factors of 312, we will follow a systematic approach. Factors are numbers that can be multiplied together to get the original number. Here are the steps to find the factors of 312:
### Step 1: Start with the number 1
The first factor of any number is always 1. So, we can start by dividing 312 by 1.
**Calculation:**
\[ 312 \div 1 = 312 \]
### Step 2: Check for divisibility by 2
Next, we check if 312 is divisible by 2 (the next whole number). Since 312 is an even number, it is divisible by 2.
**Calculation:**
\[ 312 \div 2 = 156 \]
### Step 3: Check for divisibility by 3
Now, we check if 312 is divisible by 3. We can do this by adding the digits of 312 (3 + 1 + 2 = 6), and since 6 is divisible by 3, so is 312.
**Calculation:**
\[ 312 \div 3 = 104 \]
### Step 4: Check for divisibility by 4
Next, we check if 312 is divisible by 4. A number is divisible by 4 if the last two digits form a number that is divisible by 4. Here, 12 is divisible by 4.
**Calculation:**
\[ 312 \div 4 = 78 \]
### Step 5: Check for divisibility by 5
Now, we check if 312 is divisible by 5. A number is divisible by 5 if it ends in 0 or 5. Since 312 ends in 2, it is not divisible by 5.
### Step 6: Check for divisibility by 6
Next, we check if 312 is divisible by 6. A number is divisible by 6 if it is divisible by both 2 and 3. Since we already established that 312 is divisible by both, it is also divisible by 6.
**Calculation:**
\[ 312 \div 6 = 52 \]
### Step 7: Check for divisibility by 7
Now, we check if 312 is divisible by 7.
**Calculation:**
\[ 312 \div 7 \approx 44.57 \]
Since this is not a whole number, 7 is not a factor.
### Step 8: Check for divisibility by 8
Next, we check if 312 is divisible by 8.
**Calculation:**
\[ 312 \div 8 = 39 \]
### Step 9: Check for divisibility by 9
Now, we check if 312 is divisible by 9.
**Calculation:**
\[ 312 \div 9 \approx 34.67 \]
Since this is not a whole number, 9 is not a factor.
### Step 10: Check for divisibility by 10
Next, we check if 312 is divisible by 10.
**Calculation:**
\[ 312 \div 10 = 31.2 \]
Since this is not a whole number, 10 is not a factor.
### Step 11: Check for divisibility by 11
Now, we check if 312 is divisible by 11.
**Calculation:**
\[ 312 \div 11 \approx 28.36 \]
Since this is not a whole number, 11 is not a factor.
### Step 12: Check for divisibility by 12
Next, we check if 312 is divisible by 12.
**Calculation:**
\[ 312 \div 12 = 26 \]
### Step 13: Check for divisibility by 13
Now, we check if 312 is divisible by 13.
**Calculation:**
\[ 312 \div 13 = 24 \]
### Step 14: Check for divisibility by 14
Next, we check if 312 is divisible by 14.
**Calculation:**
\[ 312 \div 14 \approx 22.29 \]
Since this is not a whole number, 14 is not a factor.
### Conclusion
The factors of 312 are:
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 156, and 312.
