What is the remainder when {17^{200}} is divided by 18 ?(A) 1 (B) 2 (C) 3(D) 4

To find the remainder when \( 17^{200} \) is divided by 18, we need to use modular arithmetic. Specifically, we are interested in the value of \( 17^{200} \mod 18 \).

### Step 1: Simplify the base number modulo 18
First, observe that \( 17 \mod 18 \) is:

17 ≡ -1 (mod 18)

This is because 17 is 1 less than 18. So, we can rewrite the expression \( 17^{200} \mod 18 \) as:

\( 17^{200} \equiv (-1)^{200} \mod 18 \)

### Step 2: Simplify the exponentiation
Since \( (-1)^{200} = 1 \) (because any even power of -1 is 1), we have:

\( 17^{200} \equiv 1 \mod 18 \)

### Step 3: Conclusion
The remainder when \( 17^{200} \) is divided by 18 is 1.

Thus, the correct answer is **(A) 1**.