What is the Greatest Common Factor of 82800 and 82815?

Greatest common factor (GCF) of 82800 and 82815 is 15.

GCF(82800,82815) = 15

We will now calculate the prime factors of 82800 and 82815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82800 and 82815.

How to find the GCF of 82800 and 82815?

We will first find the prime factorization of 82800 and 82815. After we will calculate the factors of 82800 and 82815 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 82815

Prime factors of 82815 are 3, 5, 5521. Prime factorization of 82815 in exponential form is:

82815 = 3¹ × 5¹ × 5521¹

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 82815

List of positive integer factors of 82815 that divides 82800 without a remainder.

1, 3, 5, 15, 5521, 16563, 27605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82800 and 82815. The biggest common factor number is the GCF number.
So the greatest common factor 82800 and 82815 is 15.

Also check out the Least Common Multiple of 82800 and 82815