What is the Greatest Common Factor of 54400 and 54414?

Greatest common factor (GCF) of 54400 and 54414 is 2.

GCF(54400,54414) = 2

We will now calculate the prime factors of 54400 and 54414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54400 and 54414.

How to find the GCF of 54400 and 54414?

We will first find the prime factorization of 54400 and 54414. After we will calculate the factors of 54400 and 54414 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54414

Prime factors of 54414 are 2, 3, 3023. Prime factorization of 54414 in exponential form is:

54414 = 2¹ × 3² × 3023¹

Step-3: Factors of 54400

List of positive integer factors of 54400 that divides 54400 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

Step-4: Factors of 54414

List of positive integer factors of 54414 that divides 54400 without a remainder.

1, 2, 3, 6, 9, 18, 3023, 6046, 9069, 18138, 27207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54400 and 54414. The biggest common factor number is the GCF number.
So the greatest common factor 54400 and 54414 is 2.

Also check out the Least Common Multiple of 54400 and 54414