Question

Find the greatest common factor of 46 and 69. Responses 23 23 - no response given 1 1 - no response given 2 2 - no response given 46 46 - no response given

Answer 1

To find the greatest common factor (GCF) of 46 and 69, we can use the prime factorization method.

1. **Prime factorization of 46**:
- 46 is divisible by 2 (the smallest prime number):
\[
46 \div 2 = 23
\]
- 23 is a prime number.
- Therefore, the prime factorization of 46 is:
\[
46 = 2 \times 23
\]

2. **Prime factorization of 69**:
- 69 is divisible by 3 (the sum of its digits, 6 + 9 = 15, is divisible by 3):
\[
69 \div 3 = 23
\]
- Therefore, the prime factorization of 69 is:
\[
69 = 3 \times 23
\]

3. **Finding the GCF**:
- The only common prime factor between 46 and 69 is 23.

Thus, the greatest common factor (GCF) of 46 and 69 is:
\[
\boxed{23}
\]