Number families with useful properties
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Log in to continueInvestigate prime, composite, square and triangular numbers.
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3 is a prime number. How many distinct positive factors does it have?
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Answer: 2
- The positive factors are 1 and 3.
- A prime number has exactly two distinct positive factors.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Investigate prime, composite, square and triangular numbers.
Read the official VCAA curriculum description (VC2M6N02)
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- VC2M6N02-C01A prime number has exactly two distinct positive factors, 1 and itself. A composite has more than two. One is neither prime nor composite. A square array has equal row and column counts.
- VC2M6N02-C02Describing and using prime/composite structure to choose a calculation strategy.
- VC2M6N02-C03A product of two different primes has four positive factors. A prime squared has three because the middle factor repeats. A triangular array grows through rows of 1, 2, 3 and so on; two copies form a rectangle.
- VC2M6N02-C04Odd does not mean prime: an odd non-trivial factorisation proves a number is composite. Use the structure of new rows to compare triangular arrays. A square’s tile count describes area, while its outer edge count describes perimeter.
- VC2M6N02-C05Constructing representations and explaining number-family patterns.
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- D01Recognise number structuresA prime number has exactly two distinct positive factors, 1 and itself. A composite has more than two. One is neither prime nor composite. A square array has equal row and column counts.
- D02Connect factors and arraysA product of two different primes has four positive factors. A prime squared has three because the middle factor repeats. A triangular array grows through rows of 1, 2, 3 and so on; two copies form a rectangle.
- D03Explain and test a propertyOdd does not mean prime: an odd non-trivial factorisation proves a number is composite. Use the structure of new rows to compare triangular arrays. A square’s tile count describes area, while its outer edge count describes perimeter.