Question

Сколькими нулями заканчивается произведение первых 100 натуральных чисел?

Answer 1

24 нулём будет оканчиваться произведение.

Answer 2

Произведение первых 100 натуральных чисел заканчивается 24 нулями.

To arrive at this answer, we can consider the number of factors of 2 and 5 in the product of the first 100 natural numbers. Since every even number contributes at least one factor of 2, and every multiple of 5 contributes at least one factor of 5, we can count the number of multiples of 5 and multiples of 25 (which contribute an additional factor of 5) among the first 100 natural numbers.

There are 20 multiples of 5 among the first 100 natural numbers (5, 10, 15, ..., 95, 100), and 4 multiples of 25 (25, 50, 75, 100). Therefore, the product of the first 100 natural numbers has at least 24 factors of 5, which means it ends with 24 zeros.

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