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You do not necessarily need the common prime factors when finding the greatest common factor, but with large numbers or numbers for which you cannot easily determine all the factors, using prime factorization to determine the greatest common factor is the easiest method. The greatest common factor can then be determined by multiplying the common prime factors together.

For example, when trying to find the greatest common factor of 2144 and 5672, finding all their possible factors to compare could be difficult. So, it is easier to find their prime factors, determine the prime factors they have in common, and then multiply the common prime factors to get the greatest common factor.

For descriptions and examples of finding the greatest common factor, see the "Related Questions" links below.

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Q: Why do you need the common prime factors when finding the greatest common factor?

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Finding the greatest common factor helps when you are reducing fractions.

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By finding the factors in both numbers and then finding the one that is greatest in common. For example the G.C.F for 45 and 36 is 9.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as ??, because there cannot be any form of 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. Examples: The common factors of 1 and 3 are only 1; the greatest common factor is 1. The common factors of 1 and 111 are only 1; the greatest common factor is 1. Note: Since the only factor of 1 is 1, when finding the greatest common factor of 1 and another number, the only possible common factor and greatest common factor is 1.

1,2,5,10 are the common factors, and the Greatest Common Factor is 10.

The greatest common factor is the largest of the common factors.

24 is not the greatest common factor of any single number. Common factors are the factors that two or more numbers have in common. The greatest common factor is the largest factor that two or more numbers have in common. There cannot be any common factors or a greatest common factor of a single number. There must be at least two number for common factors and a greatest common factor. Example: The greatest common factor of 24 and 48 is 24. The greatest common factor of 60 and 144 is 24. The greatest common factor of 240 and 264 is 24.

At least. You can list their factors or compare their prime factorizations.

Neither 16 nor 36 have a greatest common factor. There is neither a greatest common factor nor common factors of a single number, such as 16, because there cannot be any form of 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. However, there is a greatest common factor of the pair of 16 and 36. It is 4. See the related question for an explanation on finding the greatest common factor of 16 and 36.

The common factors are: 1, 3 The Greatest Common Factor (GCF) is: 3

The common factors are: 1, 3 The Greatest Common Factor (GCF) is: 3

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 35, because there cannot be any form of 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. Examples: The common factors of 10 and 35 are 1 and 5; the greatest common factor is 5. The common factors of 21 and 35 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 45 are 1 and 5; the greatest common factor is 5. The common factors of 35 and 49 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 61 are only 1; the greatest common factor is 1.

There's no trick. Find all the factors of the numbers you want to compare. Select the ones in common. Pick the largest one. That's the greatest common factor.

Factors of 15: 1,3,5,15 Factors of 77: 1,7,11,77 Greatest common factor: 1

factors of 6 are 1,2,3,6 Factors of 8 are 1,2,4,8 The Greatest common factor is 2

Common Factors: 14,7,2,1 Greatest Common Factor: 14

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 34, because there cannot be any form of 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. Examples: The common factors of 12 and 34 are 1 and 2; the greatest common factor is 2. The common factors of 34 and 40 are 1 and 2; the greatest common factor is 2. The common factors of 34 and 85 are 1 and 17; the greatest common factor is 17. The common factors of 34 and 91 are only 1; the greatest common factor is 1.

The greatest common factor is the greatest number that divides two numbers. The procedure for finding the greatest common factor is:List the prime factors of each number.Multiply together all the factors that both the numbers have in common. If there are no common prime factors, the GCF is 1.In this case, the prime factors of 87 are 3 and 29 because 3*29 = 87 and 3 and 29 are prime.andthe prime factor of 3 is 3 because 3 is prime.Therefore, the common factors are a single prime = 3Therefore, the greatest common factor of 83 and 3 is 3.

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There is neither a greatest common factor nor common factors of a single number, such as 10, because there cannot be any form of 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 are 1, 2, 5, and 10. The prime factors of 10 are 2 and 5. Examples: The common factors of 10 and 35 are 1 and 5; the greatest common factor is 5. The common factors of 10 and 38 are 1 and 2; the greatest common factor is 2. The common factors of 10 and 90 are 1, 2, 5, and 10; the greatest common factor is 10. The common factors of 10 and 108 are 1 and 2; the greatest common factor is 2.

There is neither a greatest common factor nor common factors of a single number, such as 25, because there cannot be any form of 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 25 are 1, 5, and 25. The prime factors of 25 are 5 and 5. Examples: The common factors of 13 and 25 are only 1; the greatest common factor is 1. The common factors of 23 and 25 are only 1; the greatest common factor is 1. The common factors of 25 and 30 are 1 and 5; the greatest common factor is 5. The common factors of 25 and 42 are only 1; the greatest common factor is 1. The common factors of 25 and 50 are 1, 5, and 25; the greatest common factor is 25.

There is neither a greatest common factor nor common factors of a single number, such as 47, because there cannot be any form of 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. Examples: The common factors of 47 and 50 are only 1; the greatest common factor is 1. The common factors of 47 and 94 are 1 and 47; the greatest common factor is 47.

Answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 147, because there cannot be any form of 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. Examples: The common factors of 14 and 147 are 1 and 7; the greatest common factor is 7. The common factors of 147 and 171 are 1 and 3; the greatest common factor is 3.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 614, because there cannot be any form of 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. Examples: The common factors of 12 and 614 are 1 and 2; the greatest common factor is 2. The common factors of 19 and 614 are only 1; the greatest common factor is 1. The common factors of 614 and 921 are 1 and 307; the greatest common factor is 307.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 27, because there cannot be any form of 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. Examples: The common factors of 27 and 33 are 1 and 3; the greatest common factor is 3. The common factors of 27 and 45 are 1, 3, and 9; the greatest common factor is 9. The common factors of 27 and 29 are only 1; the greatest common factor is 1.