Final answer:
The greatest common factor (GCF) of 32, 50, and 26 is determined by identifying the highest power of prime factors they have in common. In this case, it is the number 2 because it's the only prime number all three share in their prime factorization, taken to the first power which is the least power it appears.
Step-by-step explanation:
To find the greatest common factor (GCF) of 32, 50, and 26, we need to determine which is the largest number that divides into all three numbers without leaving a remainder. We start by listing the prime factors of each number:
- 32 = 2µ
- 50 = 2 × 5²
- 26 = 2 × 13
The only prime factor common to all three numbers is 2. However, since the number 26 contains the prime factor 2 to the first power, we can only use the prime factor 2 once when finding the GCF. Thus, the GCF of 32, 50, and 26 is 2.