2A Factors and multiples CONSOLIDATING

Learning intentions for this section:

• To know what factors and multiples are

• To understand that every number has infinitely many multiples

• To be able to find factors and multiples of a number

Past, present and future learning:

• This section consolidates and extends Stage 3 concepts which are used in Stage 4

• It prepares students for future work with fractions and other important concepts

• Expertise with these concepts may be required in non-calculator examinations such as NAPLAN and industry aptitude tests

Many famous mathematicians have studied number patterns in an attempt to better understand our world and to assist with new scientific discoveries. Around 600bce, the Greeks built on the early work of the Egyptians and Babylonians. Thales of Miletus, the ‘father of Greek mathematics’, is credited for significant advances in Number Theory. One of his students, Pythagoras of Samos, went on to become one of the most well-known mathematicians to have lived. Pythagoras was primarily a religious leader, but he believed that the understanding of the world could be enhanced through the understanding of numbers. We start this chapter on Number Properties and Patterns by explaining the concepts of factors and multiples, which are key building blocks for Number Theory.

Factors of 24 are used by nurses who dispense prescription medicines in hospitals and nursing homes. For example: four times/day is every 6 hours (4 × 6 = 24); three times/ day is every 8 hours (3 × 8 = 24)

Imagine one dozen doughnuts packed into bags with 3 rows of 4 doughnuts each. Since 3 × 4 = 12, we can say that 3 and 4 are factors of 12

Purchasing ‘multiple’ packs of one dozen doughnuts could result in buying 24, 36, 48 or 60 doughnuts, depending on the number of packs. These numbers are known as multiples of 12

Lesson starter: The most factors, the most multiples

Which number that is less than 100 has the most factors?

Which number that is less than 100 has the most multiples less than 100?

Key Ideas

■ Factors of a particular number are numbers that divide exactly into that number.