The Greatest Common Factor of 6 and 9

When we talk about factors, we mean the numbers that can be multiplied to get a certain number. For instance, the factors of 6 are 1, 2, 3, and 6 since these numbers can be multiplied to give us 6. Similarly, the factors of 9 are 1, 3, and 9.

Now, the greatest common factor (GCF) of two or more numbers is the largest number that divides them evenly. To find the GCF of 6 and 9, we need to list all their factors and pick the largest one that they have in common. As we have seen above, their factors are:

– 6: 1, 2, 3, 6

– 9: 1, 3, 9

The only factor that they share is 3. Therefore, the GCF of 6 and 9 is 3. We can also write this as GCF(6, 9) = 3.

Knowing the GCF of two numbers is useful for many reasons, including:

– Simplifying fractions: We can divide both the numerator and denominator of a fraction by their GCF to get an equivalent fraction with smaller numbers. For example, if we have the fraction 12/18, we can divide both 12 and 18 by 6 (which is the GCF of 12 and 18) to get 2/3.

– Factoring polynomials: When we factor a polynomial, we look for its GCF and divide all its terms by it. This helps us simplify the polynomial and make it easier to work with.

– Finding common denominators: When adding or subtracting fractions, we need to find a common denominator for them. The easiest way to do this is by finding their GCF and multiplying the denominators by it.

In conclusion, the GCF of 6 and 9 is 3. Knowing the GCF of two or more numbers can help us simplify fractions, factor polynomials, and find common denominators.