What is the greatest common factor (HINT: It may help for you to show an example of how to find a greatest common factor)? How do you know when you have found the greatest one?
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The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest number that divides two or more numbers without leaving a remainder. To find the GCF of two or more numbers, you can follow these steps:
1. Make a list of the factors of each number.
- A factor is a number that divides evenly into another number.
- For example, to find the factors of 24, you would list: 1, 2, 3, 4, 6, 8, 12, and 24.
2. Identify the common factors shared by both numbers.
- Common factors are the numbers that appear in the lists of factors of both numbers.
- For example, if you're finding the GCF of 24 and 36, the common factors are: 1, 2, 3, 4, 6, and 12.
3. Determine the greatest common factor (GCF).
- The GCF is the largest number among the common factors.
- In our example, the GCF of 24 and 36 is 12, as it is the largest number that divides both numbers without leaving a remainder.
To know when you have found the greatest common factor, you need to ensure that you have checked all the common factors and selected the highest one. It's important to list all the factors correctly and compare them properly to identify the largest common factor. Additionally, you can check your answer by dividing both numbers by the GCF to see if it evenly divides without a remainder.
Remember that prime factorization is another method to find the GCF, which involves breaking down each number into its prime factors and then identifying the common prime factors.