Identify Multiples and Factors 4 - Reasoning

In a segment focused on identifying multiples and factors, the reasoning task examines the claim made by a student named Leanna regarding the common factors of the numbers 18 and 25. Leanna asserts that the highest common factor (HCF) of these two numbers is 1. To validate her statement, an analysis of the factors for each number is conducted. The factors of 18 are listed as 1, 2, 3, 6, 9, and 18, which are all the numbers that divide 18 without leaving a remainder. Similarly, the factors of 25 are identified as 1, 5, and 25, which are the numbers that evenly divide 25.

Upon reviewing the factors of both numbers, it is evident that the only factor they share is the number 1. No other number is common between the two sets of factors. This means that there are no common factors of 18 and 25 that are greater than 1. Therefore, the conclusion is drawn that the highest common factor of 18 and 25 is indeed 1, confirming Leanna's initial claim. To prove this, one simply needs to compare the lists of factors for each number and note that 1 is the only number that appears in both lists, which is the defining characteristic of a highest common factor when no other common factors exist.