What is the greatest common factor of 28 and \( 49 ? \)

To find the greatest common factor (GCF) of 28 and 49, we first look at their prime factorizations. The prime factorization of 28 is \( 2^2 \times 7 \), and for 49, it's \( 7^2 \). The only common prime factor is 7. Therefore, the GCF of 28 and 49 is 7. Fun fact: The concept of GCF has been around since ancient times, with mathematicians like Euclid creating algorithms to find it. It’s not just a mathematical exercise; it's a handy tool that helps in simplifying fractions—making life a tad easier! If you ever feel stuck while calculating the GCF, remember the “list it out” method! Write the factors of each number down, and then simply look for the largest number that appears in both lists. It’s a straightforward way to avoid common mistakes, like rushing through your calculations or misidentifying factors!