What is the Greatest Common Factor of 28689 and 28704?

Greatest common factor (GCF) of 28689 and 28704 is 3.

GCF(28689,28704) = 3

We will now calculate the prime factors of 28689 and 28704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28689 and 28704.

How to find the GCF of 28689 and 28704?

We will first find the prime factorization of 28689 and 28704. After we will calculate the factors of 28689 and 28704 and find the biggest common factor number .

Step-1: Prime Factorization of 28689

Prime factors of 28689 are 3, 73, 131. Prime factorization of 28689 in exponential form is:

28689 = 3¹ × 73¹ × 131¹

Step-2: Prime Factorization of 28704

Prime factors of 28704 are 2, 3, 13, 23. Prime factorization of 28704 in exponential form is:

28704 = 2⁵ × 3¹ × 13¹ × 23¹

Step-3: Factors of 28689

List of positive integer factors of 28689 that divides 28689 without a remainder.

1, 3, 73, 131, 219, 393, 9563

Step-4: Factors of 28704

List of positive integer factors of 28704 that divides 28689 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 23, 24, 26, 32, 39, 46, 48, 52, 69, 78, 92, 96, 104, 138, 156, 184, 208, 276, 299, 312, 368, 416, 552, 598, 624, 736, 897, 1104, 1196, 1248, 1794, 2208, 2392, 3588, 4784, 7176, 9568, 14352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28689 and 28704. The biggest common factor number is the GCF number.
So the greatest common factor 28689 and 28704 is 3.

Also check out the Least Common Multiple of 28689 and 28704