What is the Greatest Common Factor of 82588 and 82600?

Greatest common factor (GCF) of 82588 and 82600 is 4.

GCF(82588,82600) = 4

We will now calculate the prime factors of 82588 and 82600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82588 and 82600.

How to find the GCF of 82588 and 82600?

We will first find the prime factorization of 82588 and 82600. After we will calculate the factors of 82588 and 82600 and find the biggest common factor number .

Step-1: Prime Factorization of 82588

Prime factors of 82588 are 2, 11, 1877. Prime factorization of 82588 in exponential form is:

82588 = 2² × 11¹ × 1877¹

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 82588

List of positive integer factors of 82588 that divides 82588 without a remainder.

1, 2, 4, 11, 22, 44, 1877, 3754, 7508, 20647, 41294

Step-4: Factors of 82600

List of positive integer factors of 82600 that divides 82588 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 82588 and 82600. The biggest common factor number is the GCF number.
So the greatest common factor 82588 and 82600 is 4.

Also check out the Least Common Multiple of 82588 and 82600