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Fluffy Ears last won the day on December 5 2011
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Factorise them completely:
16: 2 X 2 X 2 X 2
24: 2 X 2 X 2 X 3
Let me put them in a more obvious position
16: (2 X 2 X 2) X 2
24: (2 X 2 X 2) X 3
Note that the front are exactly the same factors.
So the gcf of this is 2 X 2 X 2 = 8.