`(5^(250))/(250)` find R.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the remainder \( R \) when \( \frac{5^{250}}{250} \) is calculated, we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression \( \frac{5^{250}}{250} \).

### Step 2: Factor the Denominator
Notice that \( 250 = 2 \times 125 \). We can rewrite our expression as:
\[ \frac{5^{250}}{2 \times 125} \]

### Step 3: Break Down \( 125 \)
Since \( 125 = 5^3 \), we can rewrite the expression further:
\[ \frac{5^{250}}{2 \times 5^3} = \frac{5^{250}}{5^3} \cdot \frac{1}{2} = \frac{5^{247}}{2} \]

### Step 4: Analyze the Division
Now, we need to find the remainder when \( 5^{247} \) is divided by \( 2 \).

### Step 5: Determine the Remainder
Since \( 5 \) is an odd number, any power of \( 5 \) will also be odd. Therefore, \( 5^{247} \) is odd.

When we divide an odd number by \( 2 \), the remainder is always \( 1 \).

### Conclusion
Thus, the remainder \( R \) when \( 5^{250} \) is divided by \( 250 \) is:
\[ R = 1 \]