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If you have two numbers A and B, and A > B, then
GCF(A, B) = (A-B, B)
Thus the problem of finding the GCF of A and B has been reduced to finding the GCF of B and a smaller number, A-B. This process can be continued until the two numbers are the same: and that number is the GCF.
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What is the greatest common factor of 121 and 132?
121: 11-11 132: 2-2-3-11 Great common factor: 11 Method(s) used: # (used) The method to find the greatest common factor of numbers is to find the prime factorizations of each one, select all matching prime factors, and then multiply. # An alternative method is to find all of the factors of each, and then select the greatest number that appears in each list. # The final method only applies to some numbers; if one of the number is a factor of the other, then that number is the greatest common factor. This is because all numbers are factors of themselves, and that is their greatest factor. If it is also a factor of the other number, then it is definitely the greatest common factor.
Why does the listing method always works to find the greatest common factor?
The greatest common factor of two numbers has to show up on the lists of factors of both numbers.
Why do you need the common prime factors when finding the greatest common factor?
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.
What is the greatest common factor of 16 and 18?
The great common factor of 16 and 18 is 2.Method 1: Listing FactorsList all the factors of both numbers and the highest factor that is the same is the greatest common factor.Factors of 16: 1, 2, 4, 8Factors of 18: 1, 2, 3, 6, 9The greatest common factor is 2.Method 2: Prime FactorizationFind the prime factorization of each number. The prime numbers that the numbers all share multiply to the great common factor.16 = 2 * 2 * 2 * 218 = 2 * 3 * 316 and 18 share one 2 as a prime factor. Therefore, the greatest common factor is 2.
Greatest common factor of 45 and 20?
The greatest common factor (GCF) of 45 and 20 is 5.Prime factors:45 = 5×3×320 = 5×2×2the only prime factor in both is 5, and so the highest common factor is 5.Alternative method:45 mod 20 = 520 mod 5 = 0so HCF = 5.
