What is the Greatest Common Factor of 82784 and 82800?

Greatest common factor (GCF) of 82784 and 82800 is 16.

GCF(82784,82800) = 16

We will now calculate the prime factors of 82784 and 82800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82784 and 82800.

How to find the GCF of 82784 and 82800?

We will first find the prime factorization of 82784 and 82800. After we will calculate the factors of 82784 and 82800 and find the biggest common factor number .

Step-1: Prime Factorization of 82784

Prime factors of 82784 are 2, 13, 199. Prime factorization of 82784 in exponential form is:

82784 = 2⁵ × 13¹ × 199¹

Step-2: Prime Factorization of 82800

Prime factors of 82800 are 2, 3, 5, 23. Prime factorization of 82800 in exponential form is:

82800 = 2⁴ × 3² × 5² × 23¹

Step-3: Factors of 82784

List of positive integer factors of 82784 that divides 82784 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 199, 208, 398, 416, 796, 1592, 2587, 3184, 5174, 6368, 10348, 20696, 41392

Step-4: Factors of 82800

List of positive integer factors of 82800 that divides 82784 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 25, 30, 36, 40, 45, 46, 48, 50, 60, 69, 72, 75, 80, 90, 92, 100, 115, 120, 138, 144, 150, 180, 184, 200, 207, 225, 230, 240, 276, 300, 345, 360, 368, 400, 414, 450, 460, 552, 575, 600, 690, 720, 828, 900, 920, 1035, 1104, 1150, 1200, 1380, 1656, 1725, 1800, 1840, 2070, 2300, 2760, 3312, 3450, 3600, 4140, 4600, 5175, 5520, 6900, 8280, 9200, 10350, 13800, 16560, 20700, 27600, 41400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82784 and 82800. The biggest common factor number is the GCF number.
So the greatest common factor 82784 and 82800 is 16.

Also check out the Least Common Multiple of 82784 and 82800