GCFs

GCF stands for Greatest Common Factor. It is the largest positive integer that divides two or more integers without leaving a remainder. To find the GCF of a set of numbers, one common method is to list all the factors of each number and then identify the largest factor that appears in all lists. For example, to find the GCF of 12 and 18, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors are 1, 2, 3, and 6. The greatest of these common factors is 6, so the GCF of 12 and 18 is 6. Another method involves using prime factorization. First, find the prime factorization of each number. Then, identify the common prime factors and multiply them together. If a prime factor appears multiple times in the factorizations, use the lowest power of that factor. For instance, the prime factorization of 12 is 2^2 * 3, and the prime factorization of 18 is 2 * 3^2. The common prime factors are 2 and 3. The lowest power of 2 is 2^1, and the lowest power of 3 is 3^1. Multiplying these gives 2 * 3 = 6. The GCF is a fundamental concept in number theory and is used in various mathematical applications, including simplifying fractions.

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