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Take any four-digit number.
Create a second number by moving the first digit to the 'back of the queue' and moving the rest along.
Now add your two numbers.
I predict your answer will be a multiple of 11...
Try it a few times. Is the answer always a multiple of $11$?
Can you explain why?
Click below to see what Samira noticed:
Click below to see what Jay noticed:
Do these observations help you to explain what's going on?
What if you start with a three-digit number?
Or a five-digit number?
Or a six-digit number?
Or a 38-digit numbers ... ?
Can you prove your findings?
You may be interested in this article on Divisibility Tests.
Click here for a poster of this problem.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
Is there an efficient way to work out how many factors a large number has?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.