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: \[ \boxed{23} \]