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Adding All Nine

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.

Powerful Factorial

Age 11 to 14 Challenge Level:

Each number will appear as a factor in 100!. So, for example 100! = 100x99x98x...where 22is a factor of 100, 2 is a factor of 98 and 25 is a factor of 96. Are there patterns to the powers of the number that appear as you consider each term of the factorial? Can this pattern be generalised for other numbers?