A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is :

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the problem step by step, we need to find the number based on the information provided and then determine the remainder when that number is divided by 67.

### Step 1: Understand the given information
We are given that a number \( x \) divided by 68 gives a quotient of 269 and a remainder of 0. This means that:
\[ x = 68 \times 269 + 0 \]

### Step 2: Calculate the number \( x \)
Using the equation from Step 1, we can calculate \( x \):
\[ x = 68 \times 269 \]

Now, performing the multiplication:
\[ x = 68 \times 269 = 18212 \]

### Step 3: Divide the number \( x \) by 67
Now we need to find the remainder when \( x \) (which is 18212) is divided by 67:
\[ 18212 \div 67 \]

### Step 4: Perform the division
Calculating the division:
\[ 18212 \div 67 \approx 271 \] (This is the quotient)

### Step 5: Calculate the product of the quotient and the divisor
Now, we multiply the quotient by the divisor to find the product:
\[ 271 \times 67 = 18157 \]

### Step 6: Find the remainder
Now, we subtract this product from \( x \) to find the remainder:
\[ \text{Remainder} = 18212 - 18157 = 55 \]

### Conclusion
Thus, when the number \( x \) is divided by 67, the remainder is:
\[ \text{Remainder} = 55 \]

### Final Answer
The remainder when the number is divided by 67 is **55**.

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