What is the GCF of 1 and 8?

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:

1 = None

8 = 2, 2, 2

• Identify the common prime factors:

There are no common prime factors between 1 and 8.

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

GCF(1, 8) = 1

Thus, the Greatest Common Factor of 1 and 8, using the prime factorization method, is 1.

This means 1 and 8 are relatively prime (coprime), having no common factors other than 1.

Listing All Common Factors Method

To find the Greatest Common Factor (GCF) of 1 and 8 by listing all common factors, follow these steps:

1. List all factors of each number:
   • Factors of 1: 1
   • Factors of 8: 1, 2, 4, 8
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 1 is a prime number and does not share any common factors with 8 other than 1, the GCF of 1 and 8 is: 1

This means 1 and 8 are relatively prime (coprime), having no common factors other than 1.