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1) Simple, but only appropriate for small numbers:Multiply the larger of the two numbers by 1, 2, 3, etc., until you find one that is divisible by the other number.

2) Appropriate for medium-sized numbers: Factor each of the numbers into prime factors. Take each prime factor that appears in at least one of the numbers. Multiply them all together. If a prime factor appears with different exponents in the two numbers, use the LOWER of the two exponents.

3) The Euclidian algorithm, appropriate for numbers of any size. I will show it here with an example: calculate the gcf of 14 and 10.

gcf(14, 10) = gcf(10, 4) - note: 4 is the remainder of the division of 14 by 10.

gcf(10, 4) = gcf(4, 2)

gcf(4, 2) = gcf(2, 0)

gcf(2, 0) = 2 - note: whenever one of the numbers is zero, the gcf is the other number.

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Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

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Q: How can you find the gcf of 2 whole number?
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