NRICH: Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

In the interactivity below, the computer generates two random digits.
Your task is to find the largest possible three-digit number which uses the computer’s digits, and one of your own, to make a multiple of 2, 3, 4 or 6.

Can you describe a strategy that ensures your first ‘guess’ is always correct?

Something else to think about:

What is the largest possible five-digit number
divisible by 12 that you can make from the digits
1345 and one more digit?

You may find the article on Divisibility Tests helpful.

Age 11 to 14 

Multiplication & Division
Middle School, High School

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NRICH (University of Cambridge)

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Online Game
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Click here for a poster of the problem.