What is the Greatest Common Factor of 68400 and 68414?

Greatest common factor (GCF) of 68400 and 68414 is 2.

GCF(68400,68414) = 2

We will now calculate the prime factors of 68400 and 68414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68400 and 68414.

How to find the GCF of 68400 and 68414?

We will first find the prime factorization of 68400 and 68414. After we will calculate the factors of 68400 and 68414 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 68414

Prime factors of 68414 are 2, 79, 433. Prime factorization of 68414 in exponential form is:

68414 = 2¹ × 79¹ × 433¹

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 68414

List of positive integer factors of 68414 that divides 68400 without a remainder.

1, 2, 79, 158, 433, 866, 34207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68400 and 68414. The biggest common factor number is the GCF number.
So the greatest common factor 68400 and 68414 is 2.

Also check out the Least Common Multiple of 68400 and 68414