What is the Greatest Common Factor of 12700 and 12714?

Greatest common factor (GCF) of 12700 and 12714 is 2.

GCF(12700,12714) = 2

We will now calculate the prime factors of 12700 and 12714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12700 and 12714.

How to find the GCF of 12700 and 12714?

We will first find the prime factorization of 12700 and 12714. After we will calculate the factors of 12700 and 12714 and find the biggest common factor number .

Step-1: Prime Factorization of 12700

Prime factors of 12700 are 2, 5, 127. Prime factorization of 12700 in exponential form is:

12700 = 2² × 5² × 127¹

Step-2: Prime Factorization of 12714

Prime factors of 12714 are 2, 3, 13, 163. Prime factorization of 12714 in exponential form is:

12714 = 2¹ × 3¹ × 13¹ × 163¹

Step-3: Factors of 12700

List of positive integer factors of 12700 that divides 12700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 127, 254, 508, 635, 1270, 2540, 3175, 6350

Step-4: Factors of 12714

List of positive integer factors of 12714 that divides 12700 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 163, 326, 489, 978, 2119, 4238, 6357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12700 and 12714. The biggest common factor number is the GCF number.
So the greatest common factor 12700 and 12714 is 2.

Also check out the Least Common Multiple of 12700 and 12714