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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!

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

### Repeaters

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.

# What an Odd Fact(or)

##### Age 11 to 14Challenge Level

What can you say about the patterns in the last digits of powers of $2$, $3$, $4$ etc?

How can you use these patterns to say what the last digits are of the numbers raised to the power $99$?

Now can you say whether the sum is divisible by $5$?