What is the Greatest Common Factor of 44800 and 44814?

Greatest common factor (GCF) of 44800 and 44814 is 14.

GCF(44800,44814) = 14

We will now calculate the prime factors of 44800 and 44814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 44800 and 44814.

How to find the GCF of 44800 and 44814?

We will first find the prime factorization of 44800 and 44814. After we will calculate the factors of 44800 and 44814 and find the biggest common factor number .

Step-1: Prime Factorization of 44800

Prime factors of 44800 are 2, 5, 7. Prime factorization of 44800 in exponential form is:

44800 = 2⁸ × 5² × 7¹

Step-2: Prime Factorization of 44814

Prime factors of 44814 are 2, 3, 7, 11, 97. Prime factorization of 44814 in exponential form is:

44814 = 2¹ × 3¹ × 7¹ × 11¹ × 97¹

Step-3: Factors of 44800

List of positive integer factors of 44800 that divides 44800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 128, 140, 160, 175, 200, 224, 256, 280, 320, 350, 400, 448, 560, 640, 700, 800, 896, 1120, 1280, 1400, 1600, 1792, 2240, 2800, 3200, 4480, 5600, 6400, 8960, 11200, 22400

Step-4: Factors of 44814

List of positive integer factors of 44814 that divides 44800 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 97, 154, 194, 231, 291, 462, 582, 679, 1067, 1358, 2037, 2134, 3201, 4074, 6402, 7469, 14938, 22407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 44800 and 44814. The biggest common factor number is the GCF number.
So the greatest common factor 44800 and 44814 is 14.

Also check out the Least Common Multiple of 44800 and 44814