2019 Mock AMC 10B Problems/Problem 19
Problem
What is the largest power of that divides ?
Solution
.
By simple mod checking, we find that
, and .
Therefore, the largest powers of that divide each of these numbers are , and . The largest power of that divides is thus .
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Solution 2
By LTE Lemma, we know that
So plugging in , and , we get so the answer is
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