Find the HCF of 13, 78 and 117 by division method.

Options

A. 7
B. 9
C. 11
D. 13

Answer

To find the HCF (Highest Common Factor) of the numbers 13, 78, and 117 using the division method, follow these steps:

### Step 1: Identify the numbers
We have three numbers: 13, 78, and 117.

### Step 2: Start with the smallest number
Since 13 is the smallest number, we will start by dividing the other two numbers (78 and 117) by 13.

### Step 3: Divide 78 by 13
- 78 ÷ 13 = 6
- Since 13 divides 78 exactly, we note that 13 is a factor of 78.

### Step 4: Divide 117 by 13
- 117 ÷ 13 = 9
- Since 13 divides 117 exactly, we note that 13 is also a factor of 117.

### Step 5: Check if there are any common factors
Now we check if there are any other common factors among the numbers:
- The factors of 13 are: 1, 13
- The factors of 78 (which can be factored as 2 × 3 × 13) are: 1, 2, 3, 6, 13, 26, 39, 78
- The factors of 117 (which can be factored as 3 × 39) are: 1, 3, 9, 13, 39, 117

### Step 6: Identify the highest common factor
The common factors of 13, 78, and 117 are: 1, 13. The highest of these is 13.

### Conclusion
Thus, the HCF of 13, 78, and 117 is **13**.

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