Solving for the Greatest Common Factor of 10 and 8

When faced with a math problem involving finding the greatest common factor (GCF), it can be helpful to break down the numbers into their prime factors. In the case of 10 and 8, we can write them as:

10 = 2 * 5

8 = 2 * 2 * 2

To find the GCF, we need to identify the shared factors. We can see that both 10 and 8 have a factor of 2, but 10 also has a factor of 5 that is not present in 8. Therefore, the GCF of 10 and 8 is simply 2.

Another method to find the GCF is to list all the factors of both numbers and then identify the largest one they have in common. For example, the factors of 10 are 1, 2, 5, and 10. The factors of 8 are 1, 2, 4, and 8. The largest factor they have in common is 2, so the GCF is 2.

In either case, we arrive at the same answer: the GCF of 10 and 8 is 2. This can be useful in simplifying fractions or reducing expressions to their simplest form.