What is the Greatest Common Factor of 21864 and 21872?

Greatest common factor (GCF) of 21864 and 21872 is 8.

GCF(21864,21872) = 8

We will now calculate the prime factors of 21864 and 21872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21864 and 21872.

How to find the GCF of 21864 and 21872?

We will first find the prime factorization of 21864 and 21872. After we will calculate the factors of 21864 and 21872 and find the biggest common factor number .

Step-1: Prime Factorization of 21864

Prime factors of 21864 are 2, 3, 911. Prime factorization of 21864 in exponential form is:

21864 = 2³ × 3¹ × 911¹

Step-2: Prime Factorization of 21872

Prime factors of 21872 are 2, 1367. Prime factorization of 21872 in exponential form is:

21872 = 2⁴ × 1367¹

Step-3: Factors of 21864

List of positive integer factors of 21864 that divides 21864 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 911, 1822, 2733, 3644, 5466, 7288, 10932

Step-4: Factors of 21872

List of positive integer factors of 21872 that divides 21864 without a remainder.

1, 2, 4, 8, 16, 1367, 2734, 5468, 10936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21864 and 21872. The biggest common factor number is the GCF number.
So the greatest common factor 21864 and 21872 is 8.

Also check out the Least Common Multiple of 21864 and 21872