What is the Greatest Common Factor of 854 and 872?

Greatest common factor (GCF) of 854 and 872 is 2.

GCF(854,872) = 2

We will now calculate the prime factors of 854 and 872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 854 and 872.

How to find the GCF of 854 and 872?

We will first find the prime factorization of 854 and 872. After we will calculate the factors of 854 and 872 and find the biggest common factor number .

Step-1: Prime Factorization of 854

Prime factors of 854 are 2, 7, 61. Prime factorization of 854 in exponential form is:

854 = 2¹ × 7¹ × 61¹

Step-2: Prime Factorization of 872

Prime factors of 872 are 2, 109. Prime factorization of 872 in exponential form is:

872 = 2³ × 109¹

Step-3: Factors of 854

List of positive integer factors of 854 that divides 854 without a remainder.

1, 2, 7, 14, 61, 122, 427

Step-4: Factors of 872

List of positive integer factors of 872 that divides 854 without a remainder.

1, 2, 4, 8, 109, 218, 436

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 854 and 872. The biggest common factor number is the GCF number.
So the greatest common factor 854 and 872 is 2.

Also check out the Least Common Multiple of 854 and 872