The greatest common factor (GCF) is the largest number that divides two or more numbers evenly. In other words, it's the biggest number that you can use to divide two or more numbers without any remainder.
For example, let's say we want to find the GCF of the numbers 12 and 18. To do this, we need to find all the factors of both numbers. Factors are the numbers that you can multiply together to get a certain number.
The factors of 12 are: 1, 2, 3, 4, 6, and 12. The factors of 18 are: 1, 2, 3, 6, 9, and 18.
The largest number that appears in both lists is 6, so the GCF of 12 and 18 is 6.
We use the GCF to simplify fractions, because it allows us to divide both the numerator and denominator by the same number, which simplifies the fraction. For example, if we wanted to simplify the fraction 12/18, we would divide both the numerator and denominator by 6 (the GCF of 12 and 18), which gives us 2/3.
So, that's the basic idea of the greatest common factor. It's the largest number that divides two or more numbers evenly, and we can use it to simplify fractions.