What is the GCF of 35 and 412?

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:

35 = 5, 7

412 = 2, 2, 103

• Identify the common prime factors:

There are no common prime factors between 35 and 412.

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

GCF(35, 412) = 1

Thus, the Greatest Common Factor of 35 and 412, using the prime factorization method, is 1.

This means 35 and 412 are relatively prime (coprime), having no common factors other than 1.

Listing All Common Factors Method

To find the Greatest Common Factor (GCF) of 35 and 412 by listing all common factors, follow these steps:

1. List all factors of each number:
   • Factors of 35: 1, 5, 7, 35
   • Factors of 412: 1, 2, 4, 103, 206, 412
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 35 is a prime number and does not share any common factors with 412 other than 1, the GCF of 35 and 412 is: 1

This means 35 and 412 are relatively prime (coprime), having no common factors other than 1.