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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Counting Factors

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

Last Digit

Age 11 to 14 Short
Challenge Level

Answer: 7


7$^1$ = 7                    8$^1$ = 8
7$^2$ = 49                  8$^2$ = 64
7$^3$ = ...3                 8$^3$ = ...2     (last digit comes from multiplying last digits)
7$^4$ = ...1                 8$^4$ = ...6
7$^5$ = ...7                 8$^5$ = ...8     (back to where we began)
7$^6$ = ...9                 8$^6$ = ...4
7$^7$ = ...3                 8$^7$ = ...2
7$^8$ = ...1                 8$^8$ = ...6

The last digits will keep looping in 4s

7$^{2000}$ = ...1              8$^{2000}$ = ...6
7$^{2016}$ = ...1              8$^{2016}$ = ...6

$\therefore$ 7$^{2016}$ + 8$^{2016}$ = ...7


You can find more short problems, arranged by curriculum topic, in our short problems collection.