To find the greatest common factor (GCF) of two or more numbers, you can use one of the following common methods:
1. Listing Factors Method
- List all the factors of each number.
- Identify the common factors among the lists.
- The greatest common factor is the largest number that appears in all lists.
Example:
Find the GCF of 30 and 42.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Common factors: 1, 2, 3, 6
GCF = 6 (largest common factor)
2. Prime Factorization Method
- Break each number down into its prime factors.
- Identify the common prime factors.
- Multiply these common primes to get the GCF.
Example:
Find the GCF of 12 and 15.
12 = 2 × 2 × 3
15 = 3 × 5
Common prime factor: 3
GCF = 3
3. Division Method (Euclid's Algorithm)
- Subtract the smaller number from the larger number.
- Replace the larger number with the result.
- Repeat until the remainder is zero.
- The last non-zero remainder is the GCF.
Example:
Find the GCF of 18 and 27.
27 - 18 = 9
18 - 9 = 9
9 - 9 = 0
GCF = 9
These methods work for two or more numbers, and the choice of method depends on the size of the numbers and convenience. For larger numbers, prime factorization or Euclid's algorithm is more efficient than listing all factors
