What is the Greatest Common Factor of 26875 and 26880?

Greatest common factor (GCF) of 26875 and 26880 is 5.

GCF(26875,26880) = 5

We will now calculate the prime factors of 26875 and 26880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26875 and 26880.

How to find the GCF of 26875 and 26880?

We will first find the prime factorization of 26875 and 26880. After we will calculate the factors of 26875 and 26880 and find the biggest common factor number .

Step-1: Prime Factorization of 26875

Prime factors of 26875 are 5, 43. Prime factorization of 26875 in exponential form is:

26875 = 5⁴ × 43¹

Step-2: 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-3: Factors of 26875

List of positive integer factors of 26875 that divides 26875 without a remainder.

1, 5, 25, 43, 125, 215, 625, 1075, 5375

Step-4: Factors of 26880

List of positive integer factors of 26880 that divides 26875 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26875 and 26880. The biggest common factor number is the GCF number.
So the greatest common factor 26875 and 26880 is 5.

Also check out the Least Common Multiple of 26875 and 26880