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Factoring and More Factoring

Source: 2017 AMC 8 #7

November 22, 2017
AMC 8

Problem Statement

Let ZZ be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of ZZ? <spanclass=latexbold>(A)</span>11<spanclass=latexbold>(B)</span>19<spanclass=latexbold>(C)</span>101<spanclass=latexbold>(D)</span>111<spanclass=latexbold>(E)</span>1111<span class='latex-bold'>(A) </span>11\qquad<span class='latex-bold'>(B) </span>19\qquad<span class='latex-bold'>(C) </span>101\qquad<span class='latex-bold'>(D) </span>111\qquad<span class='latex-bold'>(E) </span>1111