What is the Greatest Common Factor of 82580 and 82600?

Greatest common factor (GCF) of 82580 and 82600 is 20.

GCF(82580,82600) = 20

We will now calculate the prime factors of 82580 and 82600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82580 and 82600.

How to find the GCF of 82580 and 82600?

We will first find the prime factorization of 82580 and 82600. After we will calculate the factors of 82580 and 82600 and find the biggest common factor number .

Step-1: Prime Factorization of 82580

Prime factors of 82580 are 2, 5, 4129. Prime factorization of 82580 in exponential form is:

82580 = 2² × 5¹ × 4129¹

Step-2: Prime Factorization of 82600

Prime factors of 82600 are 2, 5, 7, 59. Prime factorization of 82600 in exponential form is:

82600 = 2³ × 5² × 7¹ × 59¹

Step-3: Factors of 82580

List of positive integer factors of 82580 that divides 82580 without a remainder.

1, 2, 4, 5, 10, 20, 4129, 8258, 16516, 20645, 41290

Step-4: Factors of 82600

List of positive integer factors of 82600 that divides 82580 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 59, 70, 100, 118, 140, 175, 200, 236, 280, 295, 350, 413, 472, 590, 700, 826, 1180, 1400, 1475, 1652, 2065, 2360, 2950, 3304, 4130, 5900, 8260, 10325, 11800, 16520, 20650, 41300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82580 and 82600. The biggest common factor number is the GCF number.
So the greatest common factor 82580 and 82600 is 20.

Also check out the Least Common Multiple of 82580 and 82600