Find the Greatest common factor of:
`72 and 112`

Options

A. `2, 5, 8`
B. `2, 4, 8`
C. `2, 4, 9`
D. `2, 4, 10`

Answer

To find the Greatest Common Factor (GCF) of the numbers 72 and 112, we can use the long division method. Here’s a step-by-step solution:

### Step 1: Identify the two numbers
We have two numbers: 72 and 112. We will use the long division method to find their GCF.

### Step 2: Divide the larger number by the smaller number
Divide 112 by 72.

- **Calculation**:
- 112 ÷ 72 = 1 (since 72 goes into 112 only once)
- Remainder = 112 - (72 × 1) = 112 - 72 = 40

### Step 3: Replace the larger number with the remainder
Now, we replace 112 with the remainder 40 and divide the previous divisor (72) by this new remainder (40).

### Step 4: Divide the previous divisor by the remainder
Now we divide 72 by 40.

- **Calculation**:
- 72 ÷ 40 = 1 (since 40 goes into 72 only once)
- Remainder = 72 - (40 × 1) = 72 - 40 = 32

### Step 5: Repeat the process
Now, we take the last remainder (40) and divide it by the new remainder (32).

- **Calculation**:
- 40 ÷ 32 = 1 (since 32 goes into 40 only once)
- Remainder = 40 - (32 × 1) = 40 - 32 = 8

### Step 6: Continue dividing until the remainder is zero
Now, we take 32 and divide it by the last remainder (8).

- **Calculation**:
- 32 ÷ 8 = 4 (since 8 goes into 32 exactly four times)
- Remainder = 32 - (8 × 4) = 32 - 32 = 0

### Step 7: Identify the GCF
Since we have reached a remainder of 0, the last non-zero remainder is the GCF.

- The GCF of 72 and 112 is **8**.

### Final Answer:
The Greatest Common Factor of 72 and 112 is **8**.

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