Prime decomposition: Understanding uniqueness

This study investigates procedural and conceptual aspects in preservice elementary school teachers ’ understanding of the Fundamental Theorem of Arithmetic. The data were col-lected by the means of a written questionnaire and individual interviews. The results suggest that the idea of the uniqueness of prime decomposition is very difficult to grasp. Participants ’ responses indicated, either implicitly or explicitly. that a possibility of alter-native prime decompositions was often not overruled. and this influenced students ’ ability to make inferences regarding factors and divisors of natural numbers. Some pedagogical implications are discussed. Andy was asked whether 17 ’ was a square number. After calculating 17 ’ and observing that its square root was not an integer, Andy gave a negative answer. Patty was asked whether 11 was a divisor of M, where M = 3 ” X 52 X 7. After calculating the number M and dividing the product by 11, Patty reached her negative conclusion. Bob was asked whether K could have 13 as a divisor, where K = 16,199 = 97 X 167 and 97,167 are both primes. He claimed it was quite possible because K ended with 9, but had actually to perform division to infe