The cognitive determinants of number series completion performance were studied by presenting a systematic set of problems to adults and to children of high and average intelligence, grades 4 and 5. Pearson correlations between these problems and the number series on the Cognitive Abilities Test were .51, .78 and .43 for the average intelligence, high intelligence, and adult groups, respectively. In each group, a combination of content and procedural knowledge factors accounted for 75% of the variance in item solution difficulty. The content factors involved understanding the sequential nature of numbers, and recognizing and executing arithmetic operations. Procedural factors were routines that established the pattern of arithmetic operation in sequence, for memory storage and recall. The most critical processing demand affecting successful performance was the amount of solution-related information to be assembled and managed in working memory. The content and procedural knowledge factors differentiated adults from children, while only content knowledge seemed to differentiate among IQ levels in children. (Author/CP)