Prime Factorization Method
There are multiple ways to find the greatest common factor of given integers. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD.
- Find the prime factorization of each number:
24 = 2, 2, 2, 3
684 = 2, 2, 3, 3, 19
- Identify the common prime factors between 24 and 684: 2, 2, 3
- To find GCF multiply the common prime factors: GCF(24, 684) = 12
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Listing All Common Factors Method
To find the Greatest Common Factor (GCF) of 24 and 684 by listing all common factors, follow these steps:
- List all factors of each number:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 684: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
- Identify the common factors of 24 and 684: 1, 2, 3, 4, 6, 12
- Determine the greatest common factor:
- The greatest common factor is the largest number in the list of common factors, i.e. 12
So, the Greatest Common Factor (GCF) of 24 and 684 is 12.