What is the Greatest Common Factor of 864 and 872?

Greatest common factor (GCF) of 864 and 872 is 8.

GCF(864,872) = 8

We will now calculate the prime factors of 864 and 872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 864 and 872.

How to find the GCF of 864 and 872?

We will first find the prime factorization of 864 and 872. After we will calculate the factors of 864 and 872 and find the biggest common factor number .

Step-1: Prime Factorization of 864

Prime factors of 864 are 2, 3. Prime factorization of 864 in exponential form is:

864 = 2⁵ × 3³

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 864

List of positive integer factors of 864 that divides 864 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432

Step-4: Factors of 872

List of positive integer factors of 872 that divides 864 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 864 and 872. The biggest common factor number is the GCF number.
So the greatest common factor 864 and 872 is 8.

Also check out the Least Common Multiple of 864 and 872