What is the Greatest Common Factor of 872 and 880?

Greatest common factor (GCF) of 872 and 880 is 8.

GCF(872,880) = 8

We will now calculate the prime factors of 872 and 880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 872 and 880.

How to find the GCF of 872 and 880?

We will first find the prime factorization of 872 and 880. After we will calculate the factors of 872 and 880 and find the biggest common factor number .

Step-1: Prime Factorization of 872

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

872 = 2³ × 109¹

Step-2: Prime Factorization of 880

Prime factors of 880 are 2, 5, 11. Prime factorization of 880 in exponential form is:

880 = 2⁴ × 5¹ × 11¹

Step-3: Factors of 872

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

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

Step-4: Factors of 880

List of positive integer factors of 880 that divides 872 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 872 and 880. The biggest common factor number is the GCF number.
So the greatest common factor 872 and 880 is 8.

Also check out the Least Common Multiple of 872 and 880