Question

Which expression can have a remainder greater than 7.
3,085 ÷ 2, 5,427 ÷ 4, 9,406 ÷ 5 or 4,337 ÷ 9?

Answer 1

To find out which expression can have a remainder greater than 7, we need to calculate the remainders for each division.

1. **For \(3,085 \div 2\)**:
- 2 goes into 3,085, which is an even number, so we can check the remainder:
- \( 3,085 \mod 2 = 1\) (as any odd number will have a remainder of 1 when divided by 2).

2. **For \(5,427 \div 4\)**:
- Divide \(5,427\) by \(4\):
- \(5,427 \mod 4\):
- When we divide \(5,427\), the last two digits are \(27\).
- \( 27 \div 4 = 6\) remainder \(3\) (since \(4 \times 6 = 24\)).
- Thus, \(5,427 \mod 4 = 3\).

3. **For \(9,406 \div 5\)**:
- Find \( 9,406 \mod 5\):
- The last digit is \(6\).
- \(6 \div 5 = 1\) remainder \(1\).
- Thus, \(9,406 \mod 5 = 1\).

4. **For \(4,337 \div 9\)**:
- Now, find \( 4,337 \mod 9\):
- The sum of the digits of \(4,337\) is \(4 + 3 + 3 + 7 = 17\).
- \(17 \div 9 = 1\) remainder \(8\).
- Thus, \(4,337 \mod 9 = 8\).

Now, let's compare the remainders we calculated:

- \(3,085 \div 2\) gives a remainder of \(1\).
- \(5,427 \div 4\) gives a remainder of \(3\).
- \(9,406 \div 5\) gives a remainder of \(1\).
- \(4,337 \div 9\) gives a remainder of \(8\).

The only division that yields a remainder greater than \(7\) is:

**\(4,337 \div 9\), with a remainder of \(8\).**