What is the Greatest Common Factor of 12600 and 12614?

Greatest common factor (GCF) of 12600 and 12614 is 14.

GCF(12600,12614) = 14

We will now calculate the prime factors of 12600 and 12614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12600 and 12614.

How to find the GCF of 12600 and 12614?

We will first find the prime factorization of 12600 and 12614. After we will calculate the factors of 12600 and 12614 and find the biggest common factor number .

Step-1: Prime Factorization of 12600

Prime factors of 12600 are 2, 3, 5, 7. Prime factorization of 12600 in exponential form is:

12600 = 2³ × 3² × 5² × 7¹

Step-2: Prime Factorization of 12614

Prime factors of 12614 are 2, 7, 17, 53. Prime factorization of 12614 in exponential form is:

12614 = 2¹ × 7¹ × 17¹ × 53¹

Step-3: Factors of 12600

List of positive integer factors of 12600 that divides 12600 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 50, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 120, 126, 140, 150, 168, 175, 180, 200, 210, 225, 252, 280, 300, 315, 350, 360, 420, 450, 504, 525, 600, 630, 700, 840, 900, 1050, 1260, 1400, 1575, 1800, 2100, 2520, 3150, 4200, 6300

Step-4: Factors of 12614

List of positive integer factors of 12614 that divides 12600 without a remainder.

1, 2, 7, 14, 17, 34, 53, 106, 119, 238, 371, 742, 901, 1802, 6307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12600 and 12614. The biggest common factor number is the GCF number.
So the greatest common factor 12600 and 12614 is 14.

Also check out the Least Common Multiple of 12600 and 12614