## Lesson abstract

In this lesson students use the prime factorisation of numbers to explore all their factors. The lesson introduction is a short exploration to identify numbers that have the same number of factors. The major part of the lesson is a substantial investigation that develops a systematic method for generating all the factors of a number given its prime factorisation.

## Mathematical purpose (for students)

To discover an easy way to work out how many factors a number has.

## Mathematical purpose (for teachers)

Having completed introductory activities relating to prime factorisation in the first two lessons of this sequence, this lesson provides an opportunity for students to apply their knowledge in a substantial investigation. As a result of the activity students learn how to find the number of factors of a number and to generate a complete list of factors from the number’s prime factorisation.

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