What is the Greatest Common Factor of 82600 and 82614?

Greatest common factor (GCF) of 82600 and 82614 is 14.

GCF(82600,82614) = 14

We will now calculate the prime factors of 82600 and 82614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82600 and 82614.

How to find the GCF of 82600 and 82614?

We will first find the prime factorization of 82600 and 82614. After we will calculate the factors of 82600 and 82614 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 82614

Prime factors of 82614 are 2, 3, 7, 281. Prime factorization of 82614 in exponential form is:

82614 = 2¹ × 3¹ × 7² × 281¹

Step-3: Factors of 82600

List of positive integer factors of 82600 that divides 82600 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

Step-4: Factors of 82614

List of positive integer factors of 82614 that divides 82600 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 281, 294, 562, 843, 1686, 1967, 3934, 5901, 11802, 13769, 27538, 41307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82600 and 82614. The biggest common factor number is the GCF number.
So the greatest common factor 82600 and 82614 is 14.

Also check out the Least Common Multiple of 82600 and 82614