If 60 , 82 and 126 are each divided by a number , then the remainder is the same in each case . The greatest possible value of the divisor is

Options

A. 16
B. 8
C. 22
D. 11

Answer

To find the greatest possible value of the divisor that gives the same remainder when dividing the numbers 60, 82, and 126, we can follow these steps:

### Step 1: Find the differences between the numbers
We first need to calculate the differences between each pair of the given numbers:
- Difference between 82 and 60:
\[ 82 - 60 = 22 \]
- Difference between 126 and 82:
\[ 126 - 82 = 44 \]
- Difference between 126 and 60:
\[ 126 - 60 = 66 \]

### Step 2: List the differences
Now we have the differences:
- 22
- 44
- 66

### Step 3: Find the HCF of the differences
Next, we need to find the highest common factor (HCF) of the differences 22, 44, and 66.

#### Step 3.1: Factor each number
- Factors of 22:
\[ 22 = 2 \times 11 \]
- Factors of 44:
\[ 44 = 2 \times 2 \times 11 = 2^2 \times 11 \]
- Factors of 66:
\[ 66 = 2 \times 3 \times 11 \]

#### Step 3.2: Identify common factors
The common factors among 22, 44, and 66 are:
- 2
- 11

### Step 4: Calculate the HCF
To find the HCF, we take the lowest power of each common factor:
- For 2, the lowest power is \(2^1\).
- For 11, the lowest power is \(11^1\).

Thus, the HCF is:
\[ HCF = 2^1 \times 11^1 = 2 \times 11 = 22 \]

### Conclusion
The greatest possible value of the divisor is:
\[ \boxed{22} \]

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