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Greatest Common Factor (GCF) A factor is a number that can divide another number. Example: The factors of 6 are 1, 2, 3, and 6. There are two ways to find the greatest common factor. If the numbers are smaller it is easiest to list out the factors of each number and look for the biggest one that they have in common. 1. List the factors of each number. 2. Find the greatest factor that they have in common. EXAMPLE: Find the GCF of 24 and 30. 24: The factors are 1, 2, 3, 4, 6, 8, 12, 24 30: The factors are 1, 2, 3, 5, 6, 10, 15, 30 The greatest common factor between 24 and 30 is 6. The second way is for numbers that are larger. 1. 2. 3. 4. Make a prime factor tree for each number. Write the prime factorization for each number without the exponents. Circle or highlight the common factors. If there are more than one common factor, multiply them together. **If they have nothing in common the GCF = 1. EXAMPLE: Find the GCF of 36 and 48. 36: The prime factorization without exponents is 2×2×3×3 48: The prime factorization without exponents is 2×2×2×2×3 The GCF = 2 × 2 × 3 = 12