To find the greatest common factor (GCF) of 31 and 93, we first need to identify the factors of both numbers.
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The factors of 31:
- Since 31 is a prime number, its only factors are 1 and 31.
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The factors of 93:
- The prime factorization of 93 is \(3 \times 31\). So, the factors of 93 are 1, 3, 31, and 93.
Next, we identify the common factors of both numbers:
- Common factors of 31 and 93 are 1 and 31.
The greatest common factor (GCF) is the largest of these common factors, which is 31.
Thus, the greatest common factor of 31 and 93 is 31.