Let’s find the greatest common factor of 26 and 14.
Before we find the greatest common factor, let’s start by finding all the factors of 26 and then all the factors of 14. We’ll start with all the factors of 26. One times 26 equals 26, so one and 26 are factors; two times 13 equals 26, so two and 13 are factors of 26. 26 is not divisible by three, four, five, six, seven, eight, nine, 10, 11, or 12, which means we found all the factors of 26.
Now onto 14, one times 14 equals 14, so one and 14 are factors of 14. Two times seven equals 14, so two and seven are factors of 14. But we’re not just looking for the factors; we’re looking for the greatest factor that 26 and 14 have in common. We want to know what’s the largest number that is a factor of both 14 and 26.
In our case, there is only one number that is common to both 14 and 26, and that is number two. Two is the only common factor and the greatest common factor of 26 and 14. The process here is to look at the list of factors from both of these numbers, two or more; sometimes we look for the greatest common factor of three or four numbers. Look on the list of the factors and then find the largest number that’s found on each list, and here that number happens to be two.