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The GCF is 3. No exponents needed.

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Q: What is the greatest common factor of 12 and 15 using exponents?
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What does cancel any common factors in fractions?

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Write the prime factorization using exponents of each number then find the greatest common factor of the numbers 12 and 15?

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The greatest common factor of 114 and 190?

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There is not a greatest common factor of a single number, such as 10,000, because there cannot be a greatest common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. The factors of 10,000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000. The prime factors of 10,000 are 2, 2, 2, 2, 5, 5, 5, and 5 or listed using exponents 24 and 54. Examples: The greatest common factor of 64 and 10,000 is 16. The greatest common factor of 750 and 10,000 is 250. The greatest common factor of 100, 4000, and 10,000 is 100.


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