Competition problem — Number theory

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Number theory Difficulty 2.3 Junior Find the answer

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

Pick one

Solution

Because we know that $5^3$ is a factor of $15!$ and $20!$ , the last three digits of both numbers is a 0, this means that the difference of the hundreds digits is also $\boxed{\textbf{(A) }0}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.