AMC10 2019 A

AMC10 2019 A · Q2

AMC10 2019 A · Q2. It mainly tests Primes & prime factorization, Digit properties (sum of digits, divisibility tests).

What is the hundreds digit of $(20! - 15!)$?

$(20! - 15!)$ 的百位数字是多少？

(A) 0 0

(B) 1 1

(D) 4 4

(E) 5 5

Answer

Correct choice: (A)

正确答案：（A）

Solution

Both 20! and 15! have at least 3 factors of 2 and at least 3 factors of 5, so both are multiples of $10^3 = 1000$ and therefore have 0s as their last three digits. The digit in the hundreds place of the difference is therefore 0 − 0 = 0.

20! 和 15! 都有至少 3 个因子 2 和至少 3 个因子 5，因此两者都是 $10^3 = 1000$ 的倍数，最后三位数字均为 0。差的百位数字因此是 $0 - 0 = 0$。

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