What is the Greatest Common Factor of 82800 and 82814?

Greatest common factor (GCF) of 82800 and 82814 is 2.

GCF(82800,82814) = 2

We will now calculate the prime factors of 82800 and 82814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82800 and 82814.

How to find the GCF of 82800 and 82814?

We will first find the prime factorization of 82800 and 82814. After we will calculate the factors of 82800 and 82814 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 82814

Prime factors of 82814 are 2, 47, 881. Prime factorization of 82814 in exponential form is:

82814 = 2¹ × 47¹ × 881¹

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 82814

List of positive integer factors of 82814 that divides 82800 without a remainder.

1, 2, 47, 94, 881, 1762, 41407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82800 and 82814. The biggest common factor number is the GCF number.
So the greatest common factor 82800 and 82814 is 2.

Also check out the Least Common Multiple of 82800 and 82814