To find the greatest common factor (GCF) of two or more numbers, you can use several methods:

1. Listing Factors Method

• List all the factors of each number.
• Identify the common factors.
• The greatest common factor is the largest factor common to all numbers.

Example:
Find the GCF of 18 and 27.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
Common factors: 1, 3, 9
GCF = 9

2. Prime Factorization Method

• Find the prime factorization of each number.
• Identify the common prime factors.
• Multiply the common prime factors to get the GCF.

Example:
Find the GCF of 168, 252, and 288.
Prime factors:
168 = 2 × 2 × 2 × 3 × 7
252 = 2 × 2 × 3 × 3 × 7
288 = 2 × 2 × 2 × 2 × 3 × 3
Common prime factors: 2 × 2 × 3 = 12
GCF = 12

3. Euclidean Algorithm (Division Method)

• Subtract the smaller number from the larger number.
• Replace the larger number with the result.
• Repeat until the remainder is zero.
• The GCF is the last non-zero remainder.

Example:
Find the GCF of 27 and 18.
27 - 18 = 9
18 - 9 = 9
9 - 9 = 0
GCF = 9

. This method is efficient for larger numbers and can be extended to more than two numbers by finding the GCF of pairs sequentially. These methods provide reliable ways to find the greatest common factor depending on the size and number of integers involved