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The "elementary" method (good for small numbers, but not for large numbers) is to compare prime factors. Find all prime factors in common and multiply.
Example: 18 = 2*3*3 and 27 = 3*3*3
Since the Common factors are 3*3 = 9, gcf(18, 27) = 9.
The better way is to use the Euclidean Algorithm, which works sort of like long division, and it is best to show it by example:
336
132
72 //132 goes into 336 twice, so subtract 132 twice from 336 to get 72
60
12
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Therefore, gcf(336, 132) = 12.
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What is the gcf of 40 and 60 and 80?
The gcf is the greatest common factor. A way of finding the gcf of three numbers is to find the gcf of the first two and then finding the gcf of that number and the third number. Because of the unique prime factorization theorem, the greatest common factor will be a product of some of the prime factors in either number. The prime factorization of 40 is 2^3 * 5 and the prime factorization of 60 is 2^2 * 3 * 5, so the gcf is going to be what is in both, or, in this case, 2^2 * 5. Th prime factorization of 80 is 2^4 * 5 and so gcf of all three numbers is 2^2 * 5, or 20.
Who is the Greek mathematician who invented an easier way of finding the GCF?
Euclid is the Greek mathematician who invented an easier way of finding the GCF.
Is there a shortcut to finding gcf of large numbers?
Yes there is
What is the GCF of 128 and 2?
The GCF is 2.
Find the gcf by finding the prime factorization of 24 and 40?
24 factors to [2 2 2 3] 40 factors to [2 2 2 5] Common factors: [2 2 2] Answer is 8◄
What are the three methods for finding the gcf of 10?
You need at least two numbers to find a GCF.
What is the gcf of 40 and 60 and 80?
The gcf is the greatest common factor. A way of finding the gcf of three numbers is to find the gcf of the first two and then finding the gcf of that number and the third number. Because of the unique prime factorization theorem, the greatest common factor will be a product of some of the prime factors in either number. The prime factorization of 40 is 2^3 * 5 and the prime factorization of 60 is 2^2 * 3 * 5, so the gcf is going to be what is in both, or, in this case, 2^2 * 5. Th prime factorization of 80 is 2^4 * 5 and so gcf of all three numbers is 2^2 * 5, or 20.
How do you show the work after finding the gcf of 12 and 78?
2 x 2 x 3 = 122 x 3 x 13 = 78Select the common factors.2 x 3 = 6, the GCF
Who is the Greek mathematician who invented an easier way of finding the GCF?
Euclid is the Greek mathematician who invented an easier way of finding the GCF.
How does finding the gcf help you solve real world problems?
Finding the LCM will help you add and subtract fractions. Finding the GCF will help you reduce fractions.
When do you use GCF and LCM?
Gcf you use when you are finding the greatest factor for the numbers. Lcm you use when you are finding the smallest multiple in the numbers factors
Why is the GCF important?
Finding the GCF will help you to simplify fractions.
What is the GCF of -6 and -2?
The GCF of -6 and -2 is 2.
What is the GCF of 6 and 40?
Factors of 6 are 1, 2, 3 and 6.Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.Common factors are 1 and 2. Therefore, the greatest common factors(gcf) is 2.Alternate method:The method used above is not useful for finding GCF of larger numbers.However, the method of prime factorization is very useful and simple for finding GCF.Prime factorization of 6 = 2x3Prime factorization of 40 = 2x2x2x5It is clear from the factorization of both numbers that 2 is the GCF.
What is the gcf of 24 and 56 by using the 2 methods?
8 because 3*8 = 24 and 7*8 = 56
What is the purpose of first finding the GCF?
The answer depends on what you are trying to achieve. there is not much point in first finding the GCF if all that you want to do is to cook some scrambled eggs!
Is there a shortcut to finding gcf of large numbers?
Yes there is
