What is the Greatest Common Factor of 12500 and 12512?

Greatest common factor (GCF) of 12500 and 12512 is 4.

GCF(12500,12512) = 4

We will now calculate the prime factors of 12500 and 12512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12500 and 12512.

How to find the GCF of 12500 and 12512?

We will first find the prime factorization of 12500 and 12512. After we will calculate the factors of 12500 and 12512 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 12512

Prime factors of 12512 are 2, 17, 23. Prime factorization of 12512 in exponential form is:

12512 = 2⁵ × 17¹ × 23¹

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 12512

List of positive integer factors of 12512 that divides 12500 without a remainder.

1, 2, 4, 8, 16, 17, 23, 32, 34, 46, 68, 92, 136, 184, 272, 368, 391, 544, 736, 782, 1564, 3128, 6256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12500 and 12512. The biggest common factor number is the GCF number.
So the greatest common factor 12500 and 12512 is 4.

Also check out the Least Common Multiple of 12500 and 12512