What is the Greatest Common Factor of 68400 and 68415?

Greatest common factor (GCF) of 68400 and 68415 is 15.

GCF(68400,68415) = 15

We will now calculate the prime factors of 68400 and 68415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68400 and 68415.

How to find the GCF of 68400 and 68415?

We will first find the prime factorization of 68400 and 68415. After we will calculate the factors of 68400 and 68415 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 68415

Prime factors of 68415 are 3, 5, 4561. Prime factorization of 68415 in exponential form is:

68415 = 3¹ × 5¹ × 4561¹

Step-3: Factors of 68400

List of positive integer factors of 68400 that divides 68400 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

Step-4: Factors of 68415

List of positive integer factors of 68415 that divides 68400 without a remainder.

1, 3, 5, 15, 4561, 13683, 22805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68400 and 68415. The biggest common factor number is the GCF number.
So the greatest common factor 68400 and 68415 is 15.

Also check out the Least Common Multiple of 68400 and 68415