What is the greatest common factor of 92 and 46?

Answer 1

To find the greatest common factor (GCF) of 92 and 46, we can use the method of finding the prime factors of each number.

1. Factor 92: \[ 92 = 2 \times 46 \] Then factor 46: \[ 46 = 2 \times 23 \] Therefore, the prime factorization of 92 is: \[ 92 = 2^2 \times 23 \]

2. Factor 46 (we already found this): \[ 46 = 2 \times 23 \]

Now we have the prime factorizations:

• \( 92 = 2^2 \times 23 \)
• \( 46 = 2^1 \times 23^1 \)

3. Identify the common factors: The common prime factors are:

   • \(2\) (minimum power is \(1\))
   • \(23\) (minimum power is \(1\))

4. Calculate the GCF: \[ \text{GCF} = 2^1 \times 23^1 = 2 \times 23 = 46 \]

Thus, the greatest common factor of 92 and 46 is \( \boxed{46} \).