What is the Greatest Common Factor of 82785 and 82800?

Greatest common factor (GCF) of 82785 and 82800 is 15.

GCF(82785,82800) = 15

We will now calculate the prime factors of 82785 and 82800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82785 and 82800.

How to find the GCF of 82785 and 82800?

We will first find the prime factorization of 82785 and 82800. After we will calculate the factors of 82785 and 82800 and find the biggest common factor number .

Step-1: Prime Factorization of 82785

Prime factors of 82785 are 3, 5, 5519. Prime factorization of 82785 in exponential form is:

82785 = 3¹ × 5¹ × 5519¹

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 82785

List of positive integer factors of 82785 that divides 82785 without a remainder.

1, 3, 5, 15, 5519, 16557, 27595

Step-4: Factors of 82800

List of positive integer factors of 82800 that divides 82785 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 82785 and 82800. The biggest common factor number is the GCF number.
So the greatest common factor 82785 and 82800 is 15.

Also check out the Least Common Multiple of 82785 and 82800