`(661xx662xx660)/(17)` find R.

Answer

To find the remainder \( R \) when \( (661 \times 662 \times 660) \) is divided by \( 17 \), we can follow these steps:

### Step 1: Calculate each number modulo 17
First, we need to find the remainder of each number when divided by 17.

- \( 661 \mod 17 \):
\[ 661 \div 17 = 38 \quad \text{(since } 17 \times 38 = 646\text{)} \]
\[ 661 - 646 = 15 \quad \Rightarrow \quad 661 \equiv 15 \mod 17 \]

- \( 662 \mod 17 \):
\[ 662 \div 17 = 38 \quad \text{(since } 17 \times 38 = 646\text{)} \]
\[ 662 - 646 = 16 \quad \Rightarrow \quad 662 \equiv 16 \mod 17 \]

- \( 660 \mod 17 \):
\[ 660 \div 17 = 38 \quad \text{(since } 17 \times 38 = 646\text{)} \]
\[ 660 - 646 = 14 \quad \Rightarrow \quad 660 \equiv 14 \mod 17 \]

### Step 2: Multiply the remainders
Now, we multiply these remainders together:
\[ (661 \times 662 \times 660) \mod 17 \equiv (15 \times 16 \times 14) \mod 17 \]

### Step 3: Calculate the product modulo 17
First, calculate \( 15 \times 16 \):
\[ 15 \times 16 = 240 \]
Now find \( 240 \mod 17 \):
\[ 240 \div 17 = 14 \quad \text{(since } 17 \times 14 = 238\text{)} \]
\[ 240 - 238 = 2 \quad \Rightarrow \quad 240 \equiv 2 \mod 17 \]

Now multiply this result by \( 14 \):
\[ (2 \times 14) \mod 17 = 28 \mod 17 \]
\[ 28 \div 17 = 1 \quad \text{(since } 17 \times 1 = 17\text{)} \]
\[ 28 - 17 = 11 \quad \Rightarrow \quad 28 \equiv 11 \mod 17 \]

### Step 4: Conclusion
Thus, the remainder \( R \) when \( (661 \times 662 \times 660) \) is divided by \( 17 \) is:
\[ \boxed{11} \]