What is the greatest common factor of 91, 26, 52, and 78?

Answer 1

To find the greatest common factor (GCF) of the numbers 91, 26, 52, and 78, we'll begin by determining the prime factorization of each number.

1. Prime factorization of 91:

   • 91 = 7 × 13

2. Prime factorization of 26:

   • 26 = 2 × 13

3. Prime factorization of 52:

   • 52 = 2^2 × 13

4. Prime factorization of 78:

   • 78 = 2 × 3 × 13

Next, we will list the prime factors of each number:

• Prime factors of 91: 7, 13
• Prime factors of 26: 2, 13
• Prime factors of 52: 2, 13
• Prime factors of 78: 2, 3, 13

Now, we find the common prime factors among all four numbers. The only prime factor that is common to all four numbers is 13.

Thus, the GCF of 91, 26, 52, and 78 is: \[ \boxed{13} \]