When 4445 is divided by 11 and 6355 is divided by 7, the difference between the remainders in both cases is

Options

A. 5
B. 6
C. 7
D. 3

Answer

To solve the problem, we need to find the remainders when 4445 is divided by 11 and when 6355 is divided by 7. Then, we will calculate the difference between these two remainders.

### Step 1: Divide 4445 by 11
1. **Perform the division**:
- 11 goes into 44 four times (11 x 4 = 44).
- Subtract 44 from 44: 44 - 44 = 0.
- Bring down the next digit (4), making it 04.
- 11 goes into 04 zero times (11 x 0 = 0).
- Subtract 0 from 04: 04 - 0 = 4.
- Bring down the next digit (5), making it 45.
- 11 goes into 45 four times (11 x 4 = 44).
- Subtract 44 from 45: 45 - 44 = 1.

2. **Remainder**: The remainder when 4445 is divided by 11 is **1**.

### Step 2: Divide 6355 by 7
1. **Perform the division**:
- 7 goes into 63 nine times (7 x 9 = 63).
- Subtract 63 from 63: 63 - 63 = 0.
- Bring down the next digit (5), making it 05.
- 7 goes into 05 zero times (7 x 0 = 0).
- Subtract 0 from 05: 05 - 0 = 5.
- Bring down the next digit (5), making it 55.
- 7 goes into 55 seven times (7 x 7 = 49).
- Subtract 49 from 55: 55 - 49 = 6.

2. **Remainder**: The remainder when 6355 is divided by 7 is **6**.

### Step 3: Calculate the difference between the remainders
- Remainder from 4445 divided by 11 = 1
- Remainder from 6355 divided by 7 = 6
- Difference = 6 - 1 = 5

### Final Answer
The difference between the remainders is **5**.

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