What is the Greatest Common Factor of 12500 and 12516?

Greatest common factor (GCF) of 12500 and 12516 is 4.

GCF(12500,12516) = 4

We will now calculate the prime factors of 12500 and 12516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12500 and 12516.

How to find the GCF of 12500 and 12516?

We will first find the prime factorization of 12500 and 12516. After we will calculate the factors of 12500 and 12516 and find the biggest common factor number .

Step-1: Prime Factorization of 12500

Prime factors of 12500 are 2, 5. Prime factorization of 12500 in exponential form is:

12500 = 2² × 5⁵

Step-2: Prime Factorization of 12516

Prime factors of 12516 are 2, 3, 7, 149. Prime factorization of 12516 in exponential form is:

12516 = 2² × 3¹ × 7¹ × 149¹

Step-3: Factors of 12500

List of positive integer factors of 12500 that divides 12500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500, 3125, 6250

Step-4: Factors of 12516

List of positive integer factors of 12516 that divides 12500 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 149, 298, 447, 596, 894, 1043, 1788, 2086, 3129, 4172, 6258

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12500 and 12516. The biggest common factor number is the GCF number.
So the greatest common factor 12500 and 12516 is 4.

Also check out the Least Common Multiple of 12500 and 12516