What is the Greatest Common Factor of 68384 and 68400?

Greatest common factor (GCF) of 68384 and 68400 is 16.

GCF(68384,68400) = 16

We will now calculate the prime factors of 68384 and 68400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68384 and 68400.

How to find the GCF of 68384 and 68400?

We will first find the prime factorization of 68384 and 68400. After we will calculate the factors of 68384 and 68400 and find the biggest common factor number .

Step-1: Prime Factorization of 68384

Prime factors of 68384 are 2, 2137. Prime factorization of 68384 in exponential form is:

68384 = 2⁵ × 2137¹

Step-2: Prime Factorization of 68400

Prime factors of 68400 are 2, 3, 5, 19. Prime factorization of 68400 in exponential form is:

68400 = 2⁴ × 3² × 5² × 19¹

Step-3: Factors of 68384

List of positive integer factors of 68384 that divides 68384 without a remainder.

1, 2, 4, 8, 16, 32, 2137, 4274, 8548, 17096, 34192

Step-4: Factors of 68400

List of positive integer factors of 68400 that divides 68384 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 48, 50, 57, 60, 72, 75, 76, 80, 90, 95, 100, 114, 120, 144, 150, 152, 171, 180, 190, 200, 225, 228, 240, 285, 300, 304, 342, 360, 380, 400, 450, 456, 475, 570, 600, 684, 720, 760, 855, 900, 912, 950, 1140, 1200, 1368, 1425, 1520, 1710, 1800, 1900, 2280, 2736, 2850, 3420, 3600, 3800, 4275, 4560, 5700, 6840, 7600, 8550, 11400, 13680, 17100, 22800, 34200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68384 and 68400. The biggest common factor number is the GCF number.
So the greatest common factor 68384 and 68400 is 16.

Also check out the Least Common Multiple of 68384 and 68400