Write the cases in long division method

Long division is a method used in arithmetic to divide one number (dividend) by another (divisor) to find the quotient and sometimes the remainder. Here's how the cases in long division typically unfold:

### 1. Divisor Greater Than Dividend

When the divisor \( D \) is greater than the dividend \( d \), the quotient \( Q \) is 0 and the remainder \( R \) is equal to the dividend \( d \):

\[ d = Q \cdot D + R \]

In this case:
- \( Q = 0 \)
- \( R = d \)

### 2. Single-Digit Divisor

If the divisor \( D \) is a single-digit number and can be divided into the first one or two digits of the dividend \( d \):

- **Steps**:
  1. Take enough digits from the left of the dividend to be equal to or greater than the divisor.
  2. Divide to get the quotient.
  3. Multiply the quotient by the divisor.
  4. Subtract the product from the digits taken.
  5. Bring down the next digit and repeat the process.

### 3. Multi-Digit Divisor

When the divisor \( D \) is a multi-digit number, such as two or more digits:

- **Steps**:
  1. Take as many digits from the left of the dividend as necessary to be equal to or greater than the divisor.
  2. Divide to find the largest quotient digit possible.
  3. Multiply the quotient digit by the divisor.
  4. Subtract the product from the digits taken to find the remainder.
  5. Bring down the next digit of the dividend and repeat the process until all digits have been processed.

### Example:

Let's divide 1234 by 12 using long division:

```
       102 remainder 10
12 ) 1234
  - 12
  ----
    3
```

- **Steps**:
  1. Divide 12 into the first two digits of 1234 (12 goes into 12 exactly once).
  2. Subtract 12 from 12 to get a remainder of 0.
  3. Bring down the next digit (3), making it 3.
  4. Divide 12 into 3, which goes 0 times with a remainder of 3.