Example: 30 and 42
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
You do a factor rainbow to find a prime factorization. You compare prime factorizations to find a greatest common factor.
7
If they have no prime factors in common, their GCF is 1.
252
2 x 2 = 42 x 5 = 10The GCF is 2.
If you construct them correctly, factor trees always work to determine the prime factorization of a number. Once you compare the prime factorizations of two or more numbers, it is relatively easy to find the greatest common factor of them from there.
The greatest common factor of 7 and 243 is 1. Prime factorizations: 7 = 7 243 = 3 x 3 x 3 x 3 common factors - no primes, so only common factor is 1: 7 x 1 = 7 243 x 1 = 243
2 x 7 = 14 5 x 7 = 35 The GCF is 7.
256
Since prime factorizations are 6 = 2 * 3, and 39 = 3 * 13, we can easily see the biggest common factor of those 6 and 39 is 3.
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.
196: 2-2-2-2-11 1078: 2-7-7-11 Greatest common factor: 22 Method(s) 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.