What is the greatest common factor of 3, 91, 96, and 83?

Answer 1

To find the greatest common factor (GCF) of the numbers 3, 91, 96, and 83, we can first examine the prime factorization of each number:

1. 3: The prime factorization is \(3\).
2. 91: The prime factorization is \(7 \times 13\).
3. 96: The prime factorization is \(2^5 \times 3\).
4. 83: The prime factorization is \(83\) (as it is a prime number).

Next, we identify the common factors among these numbers. A GCF must be a factor of all numbers involved:

• 3: The factors are \(1, 3\).
• 91: The factors are \(1, 7, 13, 91\).
• 96: The factors are \(1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96\).
• 83: The factors are \(1, 83\).

Now we look for the common factors in all four numbers:

• The only factor that appears in all of them is 1.

Therefore, the greatest common factor of 3, 91, 96, and 83 is

\[ \boxed{1} \]