Divide 53968 by 267 and check the result by the division algorithm.

Answer

To solve the problem of dividing 53968 by 267 and checking the result using the division algorithm, we will follow these steps:

### Step 1: Perform the Division
We need to divide 53968 by 267.

1. **Estimate how many times 267 fits into the leading digits of 53968.**
- 267 goes into 539 (the first three digits) approximately 2 times because 267 x 2 = 534.

2. **Subtract 534 from 539.**
- 539 - 534 = 5.

3. **Bring down the next digit (6) to make it 56.**
- Now we have 56.

4. **Estimate how many times 267 fits into 56.**
- 267 does not fit into 56, so we write 0.

5. **Bring down the next digit (8) to make it 568.**
- Now we have 568.

6. **Estimate how many times 267 fits into 568.**
- 267 goes into 568 approximately 2 times because 267 x 2 = 534.

7. **Subtract 534 from 568.**
- 568 - 534 = 34.

Now we have:
- **Quotient = 202**
- **Remainder = 34**

### Step 2: Verify using the Division Algorithm
The division algorithm states that:
\[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \]

Here:
- Dividend = 53968
- Divisor = 267
- Quotient = 202
- Remainder = 34

Now, substitute the values into the equation:
\[ 53968 = 267 \times 202 + 34 \]

### Step 3: Calculate the Right Side
1. **Calculate \( 267 \times 202 \):**
- \( 267 \times 202 = 53934 \)

2. **Add the remainder:**
- \( 53934 + 34 = 53968 \)

### Conclusion
Since both sides of the equation are equal:
\[ 53968 = 53968 \]
The result is verified.

### Final Answer
- Quotient = 202
- Remainder = 34

---