Find the common factors of `18` and `78`

Options

A. `2, 3, 6`
B. `2, 3, 9`
C. `2, 4, 6`
D. `2, 3, 8`

Answer

To find the common factors of 18 and 78, we will follow these steps:

### Step 1: Find the factors of 18
To find the factors of 18, we will list all the numbers that divide 18 without leaving a remainder.

- Start with 1: \( 18 \div 1 = 18 \) (1 is a factor)
- Next, 2: \( 18 \div 2 = 9 \) (2 is a factor)
- Next, 3: \( 18 \div 3 = 6 \) (3 is a factor)
- Next, 6: \( 18 \div 6 = 3 \) (6 is a factor)
- Next, 9: \( 18 \div 9 = 2 \) (9 is a factor)
- Finally, 18: \( 18 \div 18 = 1 \) (18 is a factor)

So, the factors of 18 are: **1, 2, 3, 6, 9, 18**.

### Step 2: Find the factors of 78
Now, we will list all the numbers that divide 78 without leaving a remainder.

- Start with 1: \( 78 \div 1 = 78 \) (1 is a factor)
- Next, 2: \( 78 \div 2 = 39 \) (2 is a factor)
- Next, 3: \( 78 \div 3 = 26 \) (3 is a factor)
- Next, 6: \( 78 \div 6 = 13 \) (6 is a factor)
- Next, 13: \( 78 \div 13 = 6 \) (13 is a factor)
- Next, 26: \( 78 \div 26 = 3 \) (26 is a factor)
- Next, 39: \( 78 \div 39 = 2 \) (39 is a factor)
- Finally, 78: \( 78 \div 78 = 1 \) (78 is a factor)

So, the factors of 78 are: **1, 2, 3, 6, 13, 26, 39, 78**.

### Step 3: Identify the common factors
Now, we will compare the factors of 18 and 78 to find the common factors.

- Factors of 18: **1, 2, 3, 6, 9, 18**
- Factors of 78: **1, 2, 3, 6, 13, 26, 39, 78**

The common factors are: **1, 2, 3, 6**.

### Step 4: Conclusion
Thus, the common factors of 18 and 78 are **1, 2, 3, and 6**. If we are asked for the highest common factor (HCF), it is **6**.

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