Factoring and Multiples

# Is there two ways for finding the greatest common factor?

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###### 2014-10-20 03:32:10

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

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## Related Questions

List the factors.Use factor trees.Use factor rainbows.

The greatest common divisor, also known as the greatest common factor is 3.There are many ways to find this including finding the prime factorization of each number.There are also many websites that will perform this operation. Calculators often find the GCF also.

Greatest common factor (GCM) is the largest number that divides into 2 or more numbers. For example: The GCM for 12 and 18 is 6. There are many ways to find the GCM. Here are ways you can find the GCM:Inverted DivisionList out all the factors of both of the numbers

24 and 25 have no common factor, other than one. There can be only one "greatest". There are two ways to solve for the greatest common factor. One way is to solve is to find the common prime factors and multiply them. So 24 = 2*2*2*3 and 25 = 5*5 Since they do not have common prime factors they do not have a GCF. Another way to solve it (just to reassure you) is to list the factors. 1. 24: 1, 2, 3, 4, 6, 8, 12, 24 25: 1, 5, 25 2. Again, you see they don't have a common factor. So technically the greatest common factor is 1.

Factor fireworks, like factor trees, rainbows, ladders, etc., are ways to notate the process of finding the prime factorization of a given number.

There are none.GCF, or Greatest Common Factor, relies on a comparison of two numbers, not just one. For instance, the GCF of 24 and 16 is 8, which can be found many different ways (one of which is shown below). Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 16: 1, 2, 4, 8, 16 As highlighted, the greatest factor which appears in both sets (i.e. the GCF) is 8.

The greatest common factor of 9, 15, and 21 is 3. We can do this many ways, but in this case it is easiest to write the factors of each number. 9 has 1,3,9 15 has 1,3,5,15 21 has 1,3,7,21 From this list, 3 is the gcf.

First, you must find the factors of each number. The factors of 49 are {1, 7, 49} because [1 x 49] and [7 x 7] are the only ways to make 49 using multiplication. The factors of 8 are {1, 2, 4, 8} because [1 x 8] and [2 x 4] are the only ways to make 8 using multiplication. The Greatest Common Factor is {1} because 1 is the only number included in both the factors of 8 and the factors of 49. Alternate Method:The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.The prime factors of 8 are 2, 2, and 2.The prime factors of 49 are 7 and 7.There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.

Factor trees are ways of finding the prime factorization of given numbers. Example: 30 and 42 30 15,2 5,3,2 42 21,2 7,3,2 Select the common factors. 2 x 3 = 6, the GCF.

The standard ways of determining the greatest common factor of three or more numbers is* to compare all their factors and choose the largest one that is common to all, or * to compare their prime factors and multiply together all the ones that are common to all, or * to determine the greatest common factor two numbers at a time.However, you can also look at the difference between the numbers being compared. The greatest common factor cannot be greater than the smallest difference between the numbers. Also, the greatest common factor must be a factor of the difference between the numbers.Example: Find the greatest common factor of 8, 10, and 14.The difference between 8 and 10 is 2, which means the greatest common factor cannot be greater than 2. (The difference between 10 and 14 is 4 and the difference between 8 and 14 is 6, both of which are divisible by 2, so 2 remains a possible greatest common factor.) So, check whether 2 evenly divides 8, 10, and 14. It does, so 2 is the greatest common factor.Example: Find the greatest common factor of 84, 91, and 105.The difference between 84 and 91 is 7, which means the greatest common factor cannot be greater than 7. (The difference between 91 and 105 is 14 and the difference between 105 and 84 is 21, both of which are divisible by 7, so 7 remains a possible greatest common factor.) So, check whether 7 evenly divides 84, 91, and 105. It does, so 7 is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.The factors of 91 are 1, 7, 13, and 91.The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.More Complex Example: Find the greatest common factor of 42, 54, and 66.The difference between 42 and 54 is 12, which is also the same difference between 54 and 66, so the greatest common factor cannot be greater than 12. So, check whether 12 evenly divides 42, 54, and 66. It does not, so try the largest factor of 12 that is less than 12, which is 6. Check whether 6 divides evenly 42, 54, and 66. It does, so 6 is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.More Complex Example: Find the greatest common factor of 36, 42, and 76.The difference between 36 and 42 is 8. The difference between 42 and 76 is 34. Since the greatest common factor must be a factor of the difference, we can examine these smaller numbers, 8 and 34, to see if they have a factor in common. The only factor they have in common (excluding 1) is 2. Since 2 evenly divides 36, 42, and 76, it is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.The factors of 76 are 1, 2, 4, 19, 38, and 76.Four Numbers Example: Find the greatest common factor of 27, 39, 54, and 60.The difference between 27 and 39 is 12. The difference between 39 and 54 is 15. The difference between 54 and 60 is 6. Since the greatest common factor must be a factor of the difference, we can examine these smaller numbers, 12, 15, and 6, to see if they have a factor in common. The only factor they have in common (excluding 1) is 3. Since 3 evenly divides 27, 39, 54, and 60, it is the greatest common factor. Here are the factors for those numbers so you can see that it is correct:The factors of 27 are 1, 3, 9, and 27.The factors of 39 are 1, 3, 13, and 39.The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.The same way as with two. You can list the factors and find the common ones or compare their prime factorizations.

The GCF of 6 and 12 is 6.You can do this in two ways:1. List all the divisors of any number:Factors, or divisors of 6 are 1, 2, 3, and 6Factors, or divisors of 12 are1, 2, 3, 4, 6, and 12The GCF is 6.2. 12/6 = 2 remainder 0.Since 12/6 gives no remainder, 6 is the GCF. the greatest common factor of 6 and 12 is 6The GCF is 3.The greatest common factor of 6 and 12 is 6.

it is simple. first lets say you have ......... 10 and 15. here is what you do.list all the ways to make 10 like the example below. then you list all of the ways to make 15. after that well i will show you.EXAMPLE. 10- 1x10,2x5 1,2,5,1015- 1x15,3x5 1,3,5,15 the greatest common factor is 5

1) The most primitive method: List several factors of each number. Check for common factors.This method is only appropriate for fairly small numbers. 2) Factoring, taking all common factors, and multiplying them. This method is appropriate for medium-sized numbers - perhaps up to a 100, or 1000. In any case, for numbers that can easily be factored. (Factoring is tricky for large numbers.) 3) Euclid's algorithm quickly gives you the greatest common factor, without actually factoring any of the numbers. This method is appropriate for numbers of any size. Example: The greatest common factor of 14 and 10 is the same as the greatest common factor of 10 and 4 - where 4 is the remainder of the division, of 14 by 10. Repeating this, gcf(10, 4) = gcf(4, 2) gcf(4, 2) = gcf (2, 0) Note that the greatest common factor of any number "n" and 0 is "n" (in this case, 2). For more than two numbers, for example, gcf(a, b, c) gcf((gcf(a, b), c). In other words, take the greatest common factor of the first two numbers, then the greatest common factor of that result with the third number, etc.

Factor trees are ways of notating the process of finding the prime factorization of a given composite number and, as such, should result in an identifiable string of prime factors.

-- "Common" means "same for both". There's no such thing as a common factor of a single number. -- Any time you're looking for the "greatest" of something, you only get one of them. If there were two greatest ones, then you'd want to know which greatest one is greater than the other greatest one. If anybody heard you asking that, they'd never talk to you again. So the question is really pretty useless, in more ways than one.

The greatest common factor of 14, 31, 65, and 69 is 1. You can find this answer in a number of different ways.First, you could notice that 31 is prime, and so its only factors are 1 and 31. Since 31 is not a factor of 19, you know that 1 is the only other possible common factor of the set.If you like, you could instead find the answer by writing the prime factorization of each number in the set. Since there are no common factors other than 1, the GCF of the set is 1.The prime factorization of 14 is 2*7The prime factorization of 31 is 1*31The prime factorization of 65 is 5*13The prime factorization of 69 is 3*23

There is an infinity of pairs of numbers with a GCF of 4. If p and P are two distinct primes, then 4p and 4P are such a pair. There are other ways to construct such pairs, but one infinity should suffice.

Multiply both the numerator (top) and the denominator (bottom) of the fraction by any non-zero integer or divide both by any common factor. You will have an equivalent fraction or equivalent ratio.

The GCF of 120 and 200 is 40One of the simplest ways to work out the gcd of 2 numbers is to take their prime factors, and multiply together the ones each number has in common. In this case,120=2x2x2x3x5, 200=2x2x2x5x5they have three 2's and one 5 in common, highlighted in bold above, and 2x2x2x5=40.

I suppose there are six ways to list them, but generally we stick to least to greatest.

Factor trees are ways of notating the process of finding a prime factorization, From there, you can determine the GCF. 105 35,3 7,5,3 225 75,3 25,3,3 5,5,3,3 Select the common factors. 3 x 5 = 15, the GCF.

you could try helping them find a common interest and having them work on it together or finding ways they are alike

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