Factors
List distinct prime factors
Identify the different prime divisors of each composite number. List each prime once, using selectable ranges through 200 and a separate key.
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List all factors
Find every positive factor of a composite number. Choose numbers up to 50, 81, 144 or 200, with 10, 15 or 20 questions and a separate answer key.
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For each number, list every positive whole number that divides it exactly. Include 1 and the number itself, and write each factor once in increasing order.
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Learning objective
What this activity builds
Find factor pairs systematically and combine them into a complete ordered list.
Worked example
List all the positive factors of 36.
1, 2, 3, 4, 6, 9, 12, 18, 36
The pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. The square pair contributes the factor 6 once, not twice.
Teaching notes
Make the practice count
- Start with 1 and the number itself, then test possible smaller factors in order. Record both members of every successful pair.
- Stop when the next possible first factor would pass its partner. All later pairs would repeat a pair already found.
- Choose the 50 range while multiplication facts are developing. Increase the range once the learner can explain how they know a list is complete.
- Every question uses a composite number. A square number can have an odd number of distinct positive factors because its central pair repeats one number.
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A useful next step
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