The product of remainders of 19009 `div` 11 and 9090 `div` 11 is

Options

A. 4
B. 5
C. 8
D. 12

Answer

To solve the problem of finding the product of the remainders of \( 19009 \div 11 \) and \( 9090 \div 11 \), we will follow these steps:

### Step 1: Calculate the remainder of \( 19009 \div 11 \)

1. **Divide 19009 by 11**:
- \( 11 \) goes into \( 190 \) (the first three digits) \( 17 \) times (since \( 11 \times 17 = 187 \)).
- Subtract \( 187 \) from \( 190 \):
\[ 190 - 187 = 3 \]
- Bring down the next digit \( 0 \) to make \( 30 \).
- \( 11 \) goes into \( 30 \) \( 2 \) times (since \( 11 \times 2 = 22 \)).
- Subtract \( 22 \) from \( 30 \):
\[ 30 - 22 = 8 \]
- Bring down the next digit \( 9 \) to make \( 89 \).
- \( 11 \) goes into \( 89 \) \( 8 \) times (since \( 11 \times 8 = 88 \)).
- Subtract \( 88 \) from \( 89 \):
\[ 89 - 88 = 1 \]
- Therefore, the remainder when \( 19009 \) is divided by \( 11 \) is \( 1 \).

### Step 2: Calculate the remainder of \( 9090 \div 11 \)

1. **Divide 9090 by 11**:
- \( 11 \) goes into \( 90 \) (the first two digits) \( 8 \) times (since \( 11 \times 8 = 88 \)).
- Subtract \( 88 \) from \( 90 \):
\[ 90 - 88 = 2 \]
- Bring down the next digit \( 0 \) to make \( 20 \).
- \( 11 \) goes into \( 20 \) \( 1 \) time (since \( 11 \times 1 = 11 \)).
- Subtract \( 11 \) from \( 20 \):
\[ 20 - 11 = 9 \]
- Bring down the next digit \( 9 \) to make \( 99 \).
- \( 11 \) goes into \( 99 \) \( 9 \) times (since \( 11 \times 9 = 99 \)).
- Subtract \( 99 \) from \( 99 \):
\[ 99 - 99 = 0 \]
- Therefore, the remainder when \( 9090 \) is divided by \( 11 \) is \( 0 \).

### Step 3: Calculate the product of the remainders

Now that we have the remainders:
- Remainder of \( 19009 \div 11 = 1 \)
- Remainder of \( 9090 \div 11 = 0 \)

The product of the remainders is:
\[ 1 \times 0 = 0 \]

### Final Answer
The product of the remainders of \( 19009 \div 11 \) and \( 9090 \div 11 \) is \( 0 \).

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