What is the remainder when
`678 + 687 + 6879 + 6890` is divided by 17 ?

Answer

To find the remainder when \( 678 + 687 + 6879 + 6890 \) is divided by 17, we can follow these steps:

### Step 1: Calculate the individual remainders
First, we will calculate the remainder of each number when divided by 17.

1. **For 678**:
\[ 678 \div 17 = 39 \quad \text{(quotient)} \]
\[ 39 \times 17 = 663 \]
\[ 678 - 663 = 15 \quad \text{(remainder)} \]

2. **For 687**:
\[ 687 \div 17 = 40 \quad \text{(quotient)} \]
\[ 40 \times 17 = 680 \]
\[ 687 - 680 = 7 \quad \text{(remainder)} \]

3. **For 6879**:
\[ 6879 \div 17 = 404 \quad \text{(quotient)} \]
\[ 404 \times 17 = 6868 \]
\[ 6879 - 6868 = 11 \quad \text{(remainder)} \]

4. **For 6890**:
\[ 6890 \div 17 = 405 \quad \text{(quotient)} \]
\[ 405 \times 17 = 6885 \]
\[ 6890 - 6885 = 5 \quad \text{(remainder)} \]

### Step 2: Sum the remainders
Now we will sum the remainders we calculated:
\[ 15 + 7 + 11 + 5 = 38 \]

### Step 3: Find the remainder of the sum when divided by 17
Next, we need to find the remainder when 38 is divided by 17:
\[ 38 \div 17 = 2 \quad \text{(quotient)} \]
\[ 2 \times 17 = 34 \]
\[ 38 - 34 = 4 \quad \text{(remainder)} \]

### Final Answer
Thus, the remainder when \( 678 + 687 + 6879 + 6890 \) is divided by 17 is \( \boxed{4} \).

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