The greatest number that divides 38 and 68 leaving 8 as remainder in each case is

Options

A. 10
B. 15
C. 60
D. 30

Answer

To find the greatest number that divides both 38 and 68, leaving a remainder of 8 in each case, we can follow these steps:

### Step 1: Subtract the remainder from both numbers
We start by subtracting the remainder (8) from both 38 and 68.

- For 38:
\[ 38 - 8 = 30 \]
- For 68:
\[ 68 - 8 = 60 \]

### Step 2: Find the HCF of the results
Next, we need to find the highest common factor (HCF) of the two results we obtained: 30 and 60.

### Step 3: Factor the numbers
We can factor both numbers to find their HCF.

- The factors of 30 are:
\[ 30 = 2 \times 3 \times 5 \]
- The factors of 60 are:
\[ 60 = 2 \times 2 \times 3 \times 5 \]

### Step 4: Identify the common factors
Now, we identify the common factors from both factorizations:
- Common factors: \(2\), \(3\), and \(5\)

### Step 5: Multiply the common factors
To find the HCF, we multiply the common factors:
\[ HCF = 2 \times 3 \times 5 = 30 \]

### Conclusion
Thus, the greatest number that divides both 38 and 68, leaving a remainder of 8, is:
\[ \text{The answer is } 30. \]