The greatest common factor (GCF) of a set of numbers is the largest positive integer that divides all of the numbers without leaving a remainder. To find the GCF of 14, 28, and 49, we can start by determining the prime factorization of each number:
- 14 = 2 × 7
- 28 = 2 × 2 × 7 (or 2² × 7)
- 49 = 7 × 7 (or 7²)
Next, we identify the common prime factors from the factorizations:
- Both 14 and 28 have the prime factors 2 and 7.
- 49 only shares the factor 7 with the other two numbers.
To find the GCF, we take the lowest power of each common factor:
- The only common prime factor is 7.
Thus, the GCF is simply 7. Therefore, the greatest common factor of 14, 28, and 49 is 7.