What is the Greatest Common Factor of 82800 and 82812?

Greatest common factor (GCF) of 82800 and 82812 is 12.

GCF(82800,82812) = 12

We will now calculate the prime factors of 82800 and 82812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82800 and 82812.

How to find the GCF of 82800 and 82812?

We will first find the prime factorization of 82800 and 82812. After we will calculate the factors of 82800 and 82812 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 82812

Prime factors of 82812 are 2, 3, 67, 103. Prime factorization of 82812 in exponential form is:

82812 = 2² × 3¹ × 67¹ × 103¹

Step-3: Factors of 82800

List of positive integer factors of 82800 that divides 82800 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

Step-4: Factors of 82812

List of positive integer factors of 82812 that divides 82800 without a remainder.

1, 2, 3, 4, 6, 12, 67, 103, 134, 201, 206, 268, 309, 402, 412, 618, 804, 1236, 6901, 13802, 20703, 27604, 41406

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82800 and 82812. The biggest common factor number is the GCF number.
So the greatest common factor 82800 and 82812 is 12.

Also check out the Least Common Multiple of 82800 and 82812