Math CentralQuandaries & Queries


Question from Cassidy, a student:

1. Number has three digits
2. The second digit is an odd number
3. The first and third digits are even numbers
4. The number can be divided by five, six, and seven with a remainder of four.

How do you even start this type of problem?

Hi Cassidy,

Start by listing the things you know that might help you:

  • a number is divisible by 5 exactly when it ends in 0 or 5,
  • a number is divisible by 6 exactly when it is divisible by 2 and by 3,
  • a number is divisible by 2 exactly when it ends in 0, 2, 4, 6, or 8,
  • a number is divisible by 3 exactly when the sum of its digits is divisible by 3.

Now combine these with what you're given;

  • the first and last digits are even,
  • the middle digit is odd.

You can take it from here. Good luck!

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