What is the Greatest Common Factor of 54395 and 54400?

Greatest common factor (GCF) of 54395 and 54400 is 5.

GCF(54395,54400) = 5

We will now calculate the prime factors of 54395 and 54400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54395 and 54400.

How to find the GCF of 54395 and 54400?

We will first find the prime factorization of 54395 and 54400. After we will calculate the factors of 54395 and 54400 and find the biggest common factor number .

Step-1: Prime Factorization of 54395

Prime factors of 54395 are 5, 11, 23, 43. Prime factorization of 54395 in exponential form is:

54395 = 5¹ × 11¹ × 23¹ × 43¹

Step-2: Prime Factorization of 54400

Prime factors of 54400 are 2, 5, 17. Prime factorization of 54400 in exponential form is:

54400 = 2⁷ × 5² × 17¹

Step-3: Factors of 54395

List of positive integer factors of 54395 that divides 54395 without a remainder.

1, 5, 11, 23, 43, 55, 115, 215, 253, 473, 989, 1265, 2365, 4945, 10879

Step-4: Factors of 54400

List of positive integer factors of 54400 that divides 54395 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 128, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 640, 680, 800, 850, 1088, 1360, 1600, 1700, 2176, 2720, 3200, 3400, 5440, 6800, 10880, 13600, 27200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54395 and 54400. The biggest common factor number is the GCF number.
So the greatest common factor 54395 and 54400 is 5.

Also check out the Least Common Multiple of 54395 and 54400