To calculate the greatest common factor (GCF) of a set of numbers, you identify the largest number that divides evenly into all the numbers in the set. Here's a step-by-step guide:
1. List the Factors of Each Number
Begin by listing all the factors (numbers that divide evenly) for each number in the set.
2. Identify Common Factors
Next, identify the factors that are common to all the numbers in the set.
3. Determine the Greatest Common Factor
Finally, select the largest number from the list of common factors. This is the GCF.
Example:
Let's find the GCF of 12, 18, and 30.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
Therefore, the GCF of 12, 18, and 30 is 6.
Alternative Method: Prime Factorization
Another method is to use prime factorization:
- Find the prime factorization of each number. Break down each number into its prime factors.
- Identify common prime factors. Find the prime factors that all the numbers share.
- Multiply the common prime factors. Multiply these common prime factors together. If there are no common prime factors, the GCF is 1.
Example using Prime Factorization (GCF of 12, 18, and 30):
- 12 = 2 x 2 x 3 = 22 x 3
- 18 = 2 x 3 x 3 = 2 x 32
- 30 = 2 x 3 x 5
Common Prime Factors: 2 and 3
Multiply: 2 x 3 = 6
The GCF is 6.
In summary, finding the GCF involves listing factors or using prime factorization to identify the largest number that divides evenly into all numbers within a set.
