Find the remainder in expression–
`(660 xx 661 xx 662)/(17)`

Options

A. 11
B. 6
C. 9
D. 12

Answer

To find the remainder of the expression \( \frac{660 \times 661 \times 662}{17} \), we can follow these steps:

### Step 1: Calculate the remainders of each number when divided by 17
First, we need to find the remainders of 660, 661, and 662 when divided by 17.

- **For 660**:
\[ 660 \div 17 = 38 \quad \text{(whole part)} \]
\[ 660 - (17 \times 38) = 660 - 646 = 14 \]
So, the remainder of 660 when divided by 17 is **14**.

- **For 661**:
\[ 661 \div 17 = 38 \quad \text{(whole part)} \]
\[ 661 - (17 \times 38) = 661 - 646 = 15 \]
So, the remainder of 661 when divided by 17 is **15**.

- **For 662**:
\[ 662 \div 17 = 38 \quad \text{(whole part)} \]
\[ 662 - (17 \times 38) = 662 - 646 = 16 \]
So, the remainder of 662 when divided by 17 is **16**.

### Step 2: Multiply the remainders
Now, we multiply the remainders we found:
\[ 14 \times 15 \times 16 \]

Calculating this step-by-step:
- First, calculate \( 14 \times 15 \):
\[ 14 \times 15 = 210 \]
- Next, multiply the result by 16:
\[ 210 \times 16 = 3360 \]

### Step 3: Find the remainder of the product when divided by 17
Now, we need to find the remainder of 3360 when divided by 17:
\[ 3360 \div 17 = 197 \quad \text{(whole part)} \]
Calculating \( 197 \times 17 \):
\[ 197 \times 17 = 3349 \]
Now, subtract this from 3360 to find the remainder:
\[ 3360 - 3349 = 11 \]

### Final Answer
Thus, the remainder when \( 660 \times 661 \times 662 \) is divided by 17 is **11**.

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