To find the Greatest Common Factor (GCF) of two numbers, you need to identify the largest number that divides both numbers evenly. Here's a breakdown of methods:
Methods to Find the GCF
1. Listing Factors
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List the factors of each number.
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Identify the common factors.
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The largest of the common factors is the GCF.
Example: Find the GCF of 12 and 18.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6
- GCF: 6
2. Prime Factorization
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Find the prime factorization of each number (express each number as a product of prime numbers).
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Identify the common prime factors.
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Multiply the common prime factors to find the GCF.
Example: Find the GCF of 18 and 24.
- Prime factorization of 18: 2 x 3 x 3
- Prime factorization of 24: 2 x 2 x 2 x 3
- Common prime factors: 2 and 3
- GCF: 2 x 3 = 6
3. Euclidean Algorithm
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Divide the larger number by the smaller number.
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Replace the larger number with the remainder.
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Repeat the process until the remainder is 0.
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The last non-zero remainder is the GCF.
Example: Find the GCF of 48 and 18.
- 48 ÷ 18 = 2 remainder 12
- 18 ÷ 12 = 1 remainder 6
- 12 ÷ 6 = 2 remainder 0
- GCF: 6
Choosing a Method
- Listing factors is best for smaller numbers.
- Prime factorization is effective for medium-sized numbers.
- Euclidean Algorithm is most efficient for larger numbers.
