Here, of course, 2 appears as a factor more often than 5. Let us calculate the number of times 5 appears as a factor: 100! has 20 numbers that are multiples of 5. Some of them (4 of them) are even multiples of 25: 25, 50, 75, and 100. In the breakdown of 100! into prime factors, one will find 5 raised to the power 24 (20 + 4 = 24). There are therefore 24 zeros at the end of 100!.

Source: Berrondom, Marie

Categories: Number sense, Factorial, Reasoning, Favorite

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