Factors
LCM and GCF of two or three numbers
Find the least common multiple and greatest common factor side by side. Choose two or three numbers per set, ranges through 120, and 10 or 12 questions.
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Find the greatest common factor
Find the greatest common factor of positive integer pairs. Choose a maximum of 24, 40, 60 or 120 and 10, 15 or 20 questions, with a separate answer key.
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Find factors of both numbers or compare their prime factorizations. Identify the largest factor they share and check that it divides each number exactly.
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What this activity builds
Distinguish common factors from all factors and select the greatest shared value.
Worked example
What is the greatest common factor of 18 and 30?
6.
The common factors are 1, 2, 3 and 6, and 6 is the largest. In prime factors, 18 = 2 × 3 × 3 and 30 = 2 × 3 × 5; the shared 2 and 3 multiply to 6.
Teaching notes
Make the practice count
- Write factors in pairs to avoid missing large factors.
- When using prime factorizations, pair only factors present in both numbers.
- Apply the result to 18/30: dividing both parts by 6 reduces it to 3/5 in one step.
- Coprime pairs are included: the only common positive factor of 8 and 15 is 1, so GCF(8, 15) = 1. A greatest common factor does not have to be greater than one.
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Preview and downloadUse a numeric GCF to simplify a fraction
Use positive whole-number pairs here. If two numbers share only the factor 1, their GCF is 1: for example, 8 and 15 are coprime. The separate combined activity offers two- or three-number sets and asks for both LCM and GCF; polynomial factoring is a different task.