Find the remainder, when (37+57+78+75+179) is divided by 17.

Options

A. 1
B. 2
C. 5
D. 7

Answer

To find the remainder when \( 37 + 57 + 78 + 75 + 179 \) is divided by \( 17 \), we can follow these steps:

### Step 1: Calculate the sum of the numbers
First, we will add the numbers together:

\[ 37 + 57 + 78 + 75 + 179 \]

Calculating this step-by-step:

1. \( 37 + 57 = 94 \)
2. \( 94 + 78 = 172 \)
3. \( 172 + 75 = 247 \)
4. \( 247 + 179 = 426 \)

So, the total sum is:

\[ 426 \]

### Step 2: Divide the sum by 17
Next, we need to divide \( 426 \) by \( 17 \) to find the remainder.

\[ 426 \div 17 \]

Calculating this division:

1. \( 17 \times 2 = 34 \) (Subtract from the first two digits of 426)
- \( 42 - 34 = 8 \)
- Bring down the next digit (6), making it \( 86 \).

2. Now divide \( 86 \) by \( 17 \):
- \( 17 \times 5 = 85 \)
- \( 86 - 85 = 1 \)

### Step 3: Conclusion
The remainder when \( 426 \) is divided by \( 17 \) is:

\[ \text{Remainder} = 1 \]

Thus, the answer is \( 1 \).

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