These tests greatly simplify the listing of factors of numbers. There are several groups of well-known divisibility tests that can check whether a number is a factor without actually performing the division. This idea leads to the classification of numbers greater than 1 as either prime or composite, and to a listing of all the factors of a number.
Whereas a number such as 31 can only be written trivially as the product 31 = 1 × 31. Some numbers, such as 30, can arise in many different ways as a product,ģ0 = 1 × 30 = 2 × 15 = 3 × 10 = 5 × 6 = 2 × 3 × 5, The factors of a number can be displayed using rectangular arrays. The number of pages in a packet of notebooks is a multiple of the number of pages in one notebook. The mass of a stack of bricks is a multiple of the mass of one brick. Even numbers are multiples of 2, and more generally, multiples arise throughout mathematics and everyday life.
Students first meet the distinction between odd numbers and even numbers in early primary school, but it is useful everywhere in mathematics. The only numbers in the module are whole numbers, apart from the final paragraphs, where fractions are used so that the fifth index law can be presented in a more satisfactory form. The ideas of this module are presented in purely arithmetical form, and no algebra is used except in some remarks that look forward to later work. This module encourages multiplicative thinking about numbers, and introduces ideas that are essential skills in fractions and algebra. Multiplication and division of whole numbers throw up many surprising things.
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