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Products to 100 (2022 AMC 8 P3)

Source:

January 25, 2022
AMC 82022 AMC 8

Problem Statement

When three positive integers a,ba, b, and cc are multiplied together, their product is 100100. Suppose a<b<ca < b < c. In how many ways can the numbers be chosen?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 4<span class='latex-bold'>(A)</span> ~0\qquad<span class='latex-bold'>(B)</span> ~1\qquad<span class='latex-bold'>(C)</span> ~2\qquad<span class='latex-bold'>(D)</span> ~3\qquad<span class='latex-bold'>(E)</span> ~4\qquad
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