To find the highest common factor (HCF) of the numbers 26, 51, and 91 using the Fundamental Theorem of Arithmetic, we first need to factor each number into its prime components.
1. **Factoring 26:**
The prime factorization of 26 is:
26 = 2 × 13
2. **Factoring 51:**
The prime factorization of 51 is:
51 = 3 × 17
3. **Factoring 91:**
The prime factorization of 91 is:
91 = 7 × 13
Next, we identify the common prime factors among these numbers. Looking at the factorizations:
- For 26: 2, 13
- For 51: 3, 17
- For 91: 7, 13
The only prime factor that appears in the factorizations of 26, 51, and 91 is 13.
Thus, the highest common factor (HCF) of 26, 51, and 91 is:
HCF = 13
In conclusion, the Fundamental Theorem of Arithmetic allows us to break down numbers into their prime factors, which simplifies the process of finding the HCF. In this case, the HCF of 26, 51, and 91 is 13.