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**Related topic**

express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another (AC9M5N02)

- using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, \(12\) blocks can form the following rectangles: \(1 \times 12, 2 \times 6\), and \(3 \times 4\)
- researching divisibility tests and explaining each rule using materials; for example, using base-\(10\) blocks to test if numbers are divisible by \(2, 5\) and \(10\)
- using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if \(89\) \(472\) is divisible by \(3\) using \(8 + 9 + 4 + 7 + 2=30\) as \(30\) is divisible by \(3\) then \(89\) \(472\) is a multiple of \(3\)
- demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of \(7\) can be formed by combining a multiple of \(2\) with the corresponding multiple of \(5\); \(3 \times 7 = 3 \times 2 + 3 \times 5\), and \(4 \times 7 = 4 \times 2 + 4 \times 5\)

Positive integers, Factors