Long division is a method of dividing large numbers by breaking the problem down into smaller, easier steps. Here's a step-by-step guide for performing long division:

### Example: Divide 457 by 3.

#### 1. **Set up the problem.**
   - Write the dividend (457) under the long division bar.
   - Write the divisor (3) outside, to the left of the bar.

#### 2. **Divide the first digit.**
   - Look at the first digit of the dividend (4). 
   - Ask: How many times does 3 go into 4? (The answer is 1, because \(3 \times 1 = 3\) and \(3 \times 2 = 6\), which is too large).
   - Write 1 above the line, directly above the 4.

#### 3. **Multiply and subtract.**
   - Multiply the divisor by the quotient: \(3 \times 1 = 3\).
   - Subtract 3 from 4: \(4 - 3 = 1\).

#### 4. **Bring down the next digit.**
   - Bring down the next digit from the dividend, which is 5, making the new number 15.

#### 5. **Divide the new number.**
   - Ask: How many times does 3 go into 15? (The answer is 5, because \(3 \times 5 = 15\)).
   - Write 5 above the line, next to the 1.

#### 6. **Multiply and subtract again.**
   - Multiply the divisor by 5: \(3 \times 5 = 15\).
   - Subtract 15 from 15: \(15 - 15 = 0\).

#### 7. **Bring down the next digit.**
   - Bring down the next digit from the dividend, which is 7, making the new number 7.

#### 8. **Divide the new number.**
   - Ask: How many times does 3 go into 7? (The answer is 2, because \(3 \times 2 = 6\)).
   - Write 2 above the line, next to the 5.

#### 9. **Multiply and subtract again.**
   - Multiply the divisor by 2: \(3 \times 2 = 6\).
   - Subtract 6 from 7: \(7 - 6 = 1\).

#### 10. **Write the remainder.**
   - Since 1 is less than 3 and no more digits are left to bring down, this is the remainder.
   - The final answer is \(152 \text{ remainder } 1\), or you can write it as \(152 \frac{1}{3}\) (if you want a fractional answer).

### Summary: 
- **457 ÷ 3 = 152 remainder 1**, or \(152 \frac{1}{3}\).

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Do you want more details or have any specific questions? Here are five related questions you can try:

1. How do you handle a decimal result in long division?
2. What happens if the divisor is larger than the first digit of the dividend?
3. Can you explain long division with polynomials?
4. How do you perform long division with a decimal divisor?
5. How does long division work with a multi-digit divisor?

**Tip:** Always check your work by multiplying the quotient by the divisor and adding the remainder to see if it equals the original dividend!

Learn how to do long division with this detailed step-by-step guide using the example 457 ÷ 3. This guide breaks down the division process, including how to handle remainders. Suitable for Grades 4-6.

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