What is the Greatest Common Factor of 68385 and 68400?

Greatest common factor (GCF) of 68385 and 68400 is 15.

GCF(68385,68400) = 15

We will now calculate the prime factors of 68385 and 68400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68385 and 68400.

How to find the GCF of 68385 and 68400?

We will first find the prime factorization of 68385 and 68400. After we will calculate the factors of 68385 and 68400 and find the biggest common factor number .

Step-1: Prime Factorization of 68385

Prime factors of 68385 are 3, 5, 47, 97. Prime factorization of 68385 in exponential form is:

68385 = 3¹ × 5¹ × 47¹ × 97¹

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 68385

List of positive integer factors of 68385 that divides 68385 without a remainder.

1, 3, 5, 15, 47, 97, 141, 235, 291, 485, 705, 1455, 4559, 13677, 22795

Step-4: Factors of 68400

List of positive integer factors of 68400 that divides 68385 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 68385 and 68400. The biggest common factor number is the GCF number.
So the greatest common factor 68385 and 68400 is 15.

Also check out the Least Common Multiple of 68385 and 68400