`(4!)/(5)` find R.

Answer

To solve the problem of finding the remainder when \( 4! \) is divided by \( 5 \), we can follow these steps:

### Step 1: Calculate \( 4! \)
The factorial of a number \( n \) (denoted as \( n! \)) is the product of all positive integers from \( 1 \) to \( n \).

For \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 \]

### Step 2: Perform the multiplication
Now, we can calculate \( 4! \):
\[ 4! = 4 \times 3 = 12 \]
\[ 12 \times 2 = 24 \]
\[ 24 \times 1 = 24 \]
Thus, \( 4! = 24 \).

### Step 3: Divide \( 4! \) by \( 5 \)
Now, we need to find the remainder when \( 24 \) is divided by \( 5 \):
\[ 24 \div 5 = 4 \quad \text{(since } 5 \times 4 = 20\text{)} \]
The quotient is \( 4 \).

### Step 4: Calculate the remainder
To find the remainder, we can subtract \( 20 \) (which is \( 5 \times 4 \)) from \( 24 \):
\[ 24 - 20 = 4 \]

### Conclusion
The remainder when \( 4! \) is divided by \( 5 \) is \( 4 \).

Thus, the final answer is:
\[ R = 4 \]

---