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10! in base 12

Source: 1970 AHSME Problem 23

March 24, 2014
AMC

Problem Statement

The number 10!10! (10(10 is written in base 10)10), when written in the base 1212 system, ends in exactly kk zeroes. The value of kk is
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>3\qquad<span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span> 5