Question

Find the greatest common factor of 46 and 69.(1 point)
Responses

2
2

1
1

23
23

46

Answer 1

To find the greatest common factor (GCF) of 46 and 69, we can start by determining the prime factorizations of both numbers:

- The prime factorization of 46 is:
\[
46 = 2 \times 23
\]

- The prime factorization of 69 is:
\[
69 = 3 \times 23
\]

Now, we can see that both numbers share a common factor of 23. To confirm it's the greatest, we can list the factors:

- Factors of 46: 1, 2, 23, 46
- Factors of 69: 1, 3, 23, 69

The greatest common factor is the highest number that appears in both lists of factors, which is 23.

Thus, the greatest common factor of 46 and 69 is \(\boxed{23}\).