What is the Greatest Common Factor of 82875 and 82880?

Greatest common factor (GCF) of 82875 and 82880 is 5.

GCF(82875,82880) = 5

We will now calculate the prime factors of 82875 and 82880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82875 and 82880.

How to find the GCF of 82875 and 82880?

We will first find the prime factorization of 82875 and 82880. After we will calculate the factors of 82875 and 82880 and find the biggest common factor number .

Step-1: Prime Factorization of 82875

Prime factors of 82875 are 3, 5, 13, 17. Prime factorization of 82875 in exponential form is:

82875 = 3¹ × 5³ × 13¹ × 17¹

Step-2: Prime Factorization of 82880

Prime factors of 82880 are 2, 5, 7, 37. Prime factorization of 82880 in exponential form is:

82880 = 2⁶ × 5¹ × 7¹ × 37¹

Step-3: Factors of 82875

List of positive integer factors of 82875 that divides 82875 without a remainder.

1, 3, 5, 13, 15, 17, 25, 39, 51, 65, 75, 85, 125, 195, 221, 255, 325, 375, 425, 663, 975, 1105, 1275, 1625, 2125, 3315, 4875, 5525, 6375, 16575, 27625

Step-4: Factors of 82880

List of positive integer factors of 82880 that divides 82875 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 37, 40, 56, 64, 70, 74, 80, 112, 140, 148, 160, 185, 224, 259, 280, 296, 320, 370, 448, 518, 560, 592, 740, 1036, 1120, 1184, 1295, 1480, 2072, 2240, 2368, 2590, 2960, 4144, 5180, 5920, 8288, 10360, 11840, 16576, 20720, 41440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82875 and 82880. The biggest common factor number is the GCF number.
So the greatest common factor 82875 and 82880 is 5.

Also check out the Least Common Multiple of 82875 and 82880