A mother is serving pizza at her son's birthday party.  After buying 5 pizzas, she must decide how many slices to divide each pizza into so that everyone at the party ends up with an equal number of slices.  There are a total of 20 children at the party, and she can choose to divide each pizza into either 6, 8, or 10 slices.  Assuming she does not want to throw away any pizza, how should many slices should she choose to divide the pizzas into to make sure everyone receives an equal amount?
Checking each possibility, we can see that dividing each pizza into 6 slices yields 5*6 = 30 total slices, dividing each pizza into 8 slices yields 5*8 = 40 total slices, and dividing each pizza into 10 slices yields 5*10 = 50 total slices.
Because each child must receive the same number of slices, the total number of slices must be evenly divisible by 20.
The only option that satisfies this requirement is dividing the pizza into 8 slices, as 40/20 = 2 slices per child. Therefore, the mother should divide each pizza into 8 slices.
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