What pair of numbers have 8 as the GCF?

Answer 1

8 and 16, and many others. For example 16 & 24, where 16 = 8 x 2 and 24 = 8 x 3. Notice that 2 and 3 are both prime numbers. So if you pick any two prime numbers (or more generally any two numbers which are coprime) then multiply each number by 8, you will have two numbers with a GCF of 8.

By coprime, these are two numbers which have a GCF of 1. Some examples of coprime numbers are 9 & 28, 100 & 51. Examine the factors of these numbers, and you'll find that the only factor common between the two numbers of each pair is 1. For example the second pair (100 and 51): 100 = 1 x 2 x 2 x 5 x 5, and 51 = 1 x 3 x 17. So the 1's are the greatest common factors (and also the only common factors). So if you multiply 8 by both of these: 8 x 100 = 800 and 8 x 51 = 408, you'll find that the greatest common factor is 8.