What is the GCF of 23 and 78?

Prime Factorization Method

There are multiple ways to find the greatest common factor of given integers. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD.

• Find the prime factorization of each number:

23 = 23

78 = 2, 3, 13

• Identify the common prime factors:

There are no common prime factors between 23 and 78.

• Since there are no common prime factors, the GCF is:

GCF(23, 78) = 1

Thus, the Greatest Common Factor of 23 and 78, using the prime factorization method, is 1.

This means 23 and 78 are relatively prime (coprime), having no common factors other than 1.

Listing All Common Factors Method

To find the Greatest Common Factor (GCF) of 23 and 78 by listing all common factors, follow these steps:

1. List all factors of each number:
   • Factors of 23: 1, 23
   • Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
2. Identify the common factors: The only common factor is 1.
3. Determine the greatest common factor:
   • The greatest common factor is the largest number in the list of common factors:
     • GCF = 1

Since 23 is a prime number and does not share any common factors with 78 other than 1, the GCF of 23 and 78 is: 1

This means 23 and 78 are relatively prime (coprime), having no common factors other than 1.