This pdf contains the introduction to the greatest common factor and examples. The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30, and 42 the GCF = 6.
1. Greatest Common Factor Factors that are shared by two or more whole numbers are called common factors. The greatest common factor is the largest of the common factors.
2. Strategies for finding the greatest common factor (GCF): 1. List all of the factors for each number 2. Write the prime factorization of each number and then calculate the product of the common prime factors
3. Determine the GCF of 32 and 80:
4. Determine the GCF of 32 and 80: Factors of 32: 1, 2, 4, 8, 16, 32 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 GCF of 32 & 80 is 16
5. Determine the GCF of 48, 60 & 84:
6. Determine the GCF of 48, 60 & 84: Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 GCF of 48, 60 & 84 is 12
7. Determine the GCF of 36 & 108:
8. Determine the GCF of 36 & 108: Prime Factorization of 36: 2x2x3x3 Prime Factorization of 108: 2x2x3x3x3 GCF of 36 & 108 = 2 x 2 x 3 x 3 GCF of 36 & 108 = 36
9. Determine the GCF of 44 & 85:
10. Determine the GCF of 44 & 85: Prime Factorization of 44: 2 x 2 x 11 Prime Factorization of 85: 5 x 17 There are no common prime factors GCF of 44 & 85 = 1
11. Determine the GCF of 45, 75 & 90:
12. Determine the GCF of 45, 75 & 90: Prime Factorization of 45: 3x3x5 Prime Factorization of 75: 3x5x5 Prime Factorization of 90: 2x3x3x5 GCF = 3 x 5 GCF of 45, 75 & 90 = 15
13. Determine the GCF of 80 & 120:
14. Determine the GCF of 80 & 120: Prime Factorization of 80: 2x2x2x2x5 Prime Factorization of 120: 2x2x2x3x5 GCF = 2 x 2 x 2 x 5 GCF of 80 & 120 = 40
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