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24 cups
1 quart = 4 cups And 1 cup = 0.25 quart.
There are 32 US fluid ounces (2 pints, or 4 cups) in 1 US quart (946.4 ml).
There are 40 Imperial fluid ounces (2 pints) in 1 Imperial quart (1,136 ml).
Note that there is no 'cup' in the Imperial system, it is best to use pints or half pints, and not 'cups'.
There are 128 oz [US] in 1 gallon [US]. Therefore,
128 / 4 = 32
It takes thirty-two 4 oz cups to form a gallon.