What is the Greatest Common Factor of 82800 and 82809?

Greatest common factor (GCF) of 82800 and 82809 is 9.

GCF(82800,82809) = 9

We will now calculate the prime factors of 82800 and 82809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82800 and 82809.

How to find the GCF of 82800 and 82809?

We will first find the prime factorization of 82800 and 82809. After we will calculate the factors of 82800 and 82809 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 82809

Prime factors of 82809 are 3, 3067. Prime factorization of 82809 in exponential form is:

82809 = 3³ × 3067¹

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 82809

List of positive integer factors of 82809 that divides 82800 without a remainder.

1, 3, 9, 27, 3067, 9201, 27603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82800 and 82809. The biggest common factor number is the GCF number.
So the greatest common factor 82800 and 82809 is 9.

Also check out the Least Common Multiple of 82800 and 82809