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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!

What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

Counting Factors

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

Powerful Factorial

Age 11 to 14 Challenge Level:

6! = 6 x 5 x 4 x 3 x 2 x 1

The highest power of 2 that divides exactly into 6! is 4. 

((6!) / (2 4 ) = 45)



What is the highest power of two that divides exactly into 100! (100 x 99 x 98 x 97 x ... x 1)?

What is the highest power of three that divides exactly into 100! ?

.......

Can you see any patterns in the calculation of the highest powers of each number that divides exactly into 100!?

Can you generalise your findings to any factorial and any number?