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 that, when divided by 68, gives a quotient of 269 and a remainder of 0. We will then use this number to find the remainder when it is divided by 67.

### Step 1: Calculate the number
According to the division formula:
\[ \text{Number} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \]
Here, the divisor is 68, the quotient is 269, and the remainder is 0. Plugging in these values, we get:
\[ \text{Number} = 68 \times 269 + 0 \]
\[ \text{Number} = 68 \times 269 \]

### Step 2: Perform the multiplication
Now we need to calculate \(68 \times 269\):
\[ 68 \times 269 = 18212 \]

### Step 3: Find the remainder when divided by 67
Now we will divide the number \(18212\) by \(67\) and find the remainder:
\[ 18212 \div 67 \]
Performing the division:
\[ 18212 = 67 \times 271 + R \]
Where \(R\) is the remainder. To find \(R\), we can calculate:
\[ 67 \times 271 = 18137 \]
Now, subtract this from \(18212\) to find the remainder:
\[ R = 18212 - 18137 = 75 \]

### Step 4: Calculate the final remainder
Now, we need to find \(75 \mod 67\):
\[ 75 = 67 \times 1 + 8 \]
So the remainder \(R\) when \(18212\) is divided by \(67\) is \(8\).

### Final Answer
The remainder when the number is divided by 67 is **8**.

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