0
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
0
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.
What is the GCF of 54 and 10?
The GCF of 10 and 54 is 2.
