What is the Greatest Common Factor of 26880 and 26900?

Greatest common factor (GCF) of 26880 and 26900 is 20.

GCF(26880,26900) = 20

We will now calculate the prime factors of 26880 and 26900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26880 and 26900.

How to find the GCF of 26880 and 26900?

We will first find the prime factorization of 26880 and 26900. After we will calculate the factors of 26880 and 26900 and find the biggest common factor number .

Step-1: Prime Factorization of 26880

Prime factors of 26880 are 2, 3, 5, 7. Prime factorization of 26880 in exponential form is:

26880 = 2⁸ × 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 26900

Prime factors of 26900 are 2, 5, 269. Prime factorization of 26900 in exponential form is:

26900 = 2² × 5² × 269¹

Step-3: Factors of 26880

List of positive integer factors of 26880 that divides 26880 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 256, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 768, 840, 896, 960, 1120, 1280, 1344, 1680, 1792, 1920, 2240, 2688, 3360, 3840, 4480, 5376, 6720, 8960, 13440

Step-4: Factors of 26900

List of positive integer factors of 26900 that divides 26880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 269, 538, 1076, 1345, 2690, 5380, 6725, 13450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26880 and 26900. The biggest common factor number is the GCF number.
So the greatest common factor 26880 and 26900 is 20.

Also check out the Least Common Multiple of 26880 and 26900