What is the Greatest Common Factor of 68380 and 68400?

Greatest common factor (GCF) of 68380 and 68400 is 20.

GCF(68380,68400) = 20

We will now calculate the prime factors of 68380 and 68400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68380 and 68400.

How to find the GCF of 68380 and 68400?

We will first find the prime factorization of 68380 and 68400. After we will calculate the factors of 68380 and 68400 and find the biggest common factor number .

Step-1: Prime Factorization of 68380

Prime factors of 68380 are 2, 5, 13, 263. Prime factorization of 68380 in exponential form is:

68380 = 2² × 5¹ × 13¹ × 263¹

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 68380

List of positive integer factors of 68380 that divides 68380 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260, 263, 526, 1052, 1315, 2630, 3419, 5260, 6838, 13676, 17095, 34190

Step-4: Factors of 68400

List of positive integer factors of 68400 that divides 68380 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 68380 and 68400. The biggest common factor number is the GCF number.
So the greatest common factor 68380 and 68400 is 20.

Also check out the Least Common Multiple of 68380 and 68400