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Clearly, one way to find the 'greatest common factor' of two or more integers would be to find all their factors, and hence all their common factors, and hence their highest common factor.
For example, find the GCF of 54 and 24.
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors of 54 and 24: 1, 2, 3, 6. So the GCF of 54 and 24 is 6.
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