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The greatest common factor of two numbers cannot be larger than the smallest difference between two of the numbers. The difference between 12 and 24 is 12. The difference between 24 and 30 is 6. The smallest difference is 6, so the greatest possible common factor is 6. Since 6 evenly divides 12, 24, and 30, the greatest common factor is 6.

Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The common factors are 1, 2, 3, and 6. Therefore, the greatest common factor is 6.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 12 are 2, 2, and 3.

The prime factors of 24 are 2, 2, 2, and 3.

The prime factors of 30 are 2, 3, and 5.

The prime factors in common are 2 and 3, so the greatest common factor is 2 x 3 = 6.

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Q: What is the greatest common factor of 12 24 and 30?

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