What is the Greatest Common Factor of 10875 and 10880?

Greatest common factor (GCF) of 10875 and 10880 is 5.

GCF(10875,10880) = 5

We will now calculate the prime factors of 10875 and 10880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10875 and 10880.

How to find the GCF of 10875 and 10880?

We will first find the prime factorization of 10875 and 10880. After we will calculate the factors of 10875 and 10880 and find the biggest common factor number .

Step-1: Prime Factorization of 10875

Prime factors of 10875 are 3, 5, 29. Prime factorization of 10875 in exponential form is:

10875 = 3¹ × 5³ × 29¹

Step-2: Prime Factorization of 10880

Prime factors of 10880 are 2, 5, 17. Prime factorization of 10880 in exponential form is:

10880 = 2⁷ × 5¹ × 17¹

Step-3: Factors of 10875

List of positive integer factors of 10875 that divides 10875 without a remainder.

1, 3, 5, 15, 25, 29, 75, 87, 125, 145, 375, 435, 725, 2175, 3625

Step-4: Factors of 10880

List of positive integer factors of 10880 that divides 10875 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 128, 136, 160, 170, 272, 320, 340, 544, 640, 680, 1088, 1360, 2176, 2720, 5440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10875 and 10880. The biggest common factor number is the GCF number.
So the greatest common factor 10875 and 10880 is 5.

Also check out the Least Common Multiple of 10875 and 10880