Question

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 \( \boxed{46} \).