What is the Greatest Common Factor of 82780 and 82800?

Greatest common factor (GCF) of 82780 and 82800 is 20.

GCF(82780,82800) = 20

We will now calculate the prime factors of 82780 and 82800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82780 and 82800.

How to find the GCF of 82780 and 82800?

We will first find the prime factorization of 82780 and 82800. After we will calculate the factors of 82780 and 82800 and find the biggest common factor number .

Step-1: Prime Factorization of 82780

Prime factors of 82780 are 2, 5, 4139. Prime factorization of 82780 in exponential form is:

82780 = 2² × 5¹ × 4139¹

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 82780

List of positive integer factors of 82780 that divides 82780 without a remainder.

1, 2, 4, 5, 10, 20, 4139, 8278, 16556, 20695, 41390

Step-4: Factors of 82800

List of positive integer factors of 82800 that divides 82780 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 82780 and 82800. The biggest common factor number is the GCF number.
So the greatest common factor 82780 and 82800 is 20.

Also check out the Least Common Multiple of 82780 and 82800