What is the Greatest Common Factor of 12782 and 12800?

Greatest common factor (GCF) of 12782 and 12800 is 2.

GCF(12782,12800) = 2

We will now calculate the prime factors of 12782 and 12800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12782 and 12800.

How to find the GCF of 12782 and 12800?

We will first find the prime factorization of 12782 and 12800. After we will calculate the factors of 12782 and 12800 and find the biggest common factor number .

Step-1: Prime Factorization of 12782

Prime factors of 12782 are 2, 7, 11, 83. Prime factorization of 12782 in exponential form is:

12782 = 2¹ × 7¹ × 11¹ × 83¹

Step-2: Prime Factorization of 12800

Prime factors of 12800 are 2, 5. Prime factorization of 12800 in exponential form is:

12800 = 2⁹ × 5²

Step-3: Factors of 12782

List of positive integer factors of 12782 that divides 12782 without a remainder.

1, 2, 7, 11, 14, 22, 77, 83, 154, 166, 581, 913, 1162, 1826, 6391

Step-4: Factors of 12800

List of positive integer factors of 12800 that divides 12782 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1280, 1600, 2560, 3200, 6400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12782 and 12800. The biggest common factor number is the GCF number.
So the greatest common factor 12782 and 12800 is 2.

Also check out the Least Common Multiple of 12782 and 12800