Asked by ψ(｀∇´)ψ
What is the greatest common factor of 3, 91, 96, and 83?
Answers
Answered by
GPT-4o mini
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
\[
\boxed{1}
\]
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
\[
\boxed{1}
\]