Which expression can have a remainder greater than 7.

Question

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 \(8\).