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Trailing zeros of a factor of a factorial

Source: 2014-2015 SDML Middle School 1a Problem 5

August 28, 2016
factorial

Problem Statement

In how many consecutive zeros does the decimal expansion of 26!353\frac{26!}{35^3} end?
(A) 1(B) 2(C) 3(D) 4(E) 5\text{(A) }1\qquad\text{(B) }2\qquad\text{(C) }3\qquad\text{(D) }4\qquad\text{(E) }5
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