What is the Greatest Common Factor of 54784 and 54800?

Greatest common factor (GCF) of 54784 and 54800 is 16.

GCF(54784,54800) = 16

We will now calculate the prime factors of 54784 and 54800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54784 and 54800.

How to find the GCF of 54784 and 54800?

We will first find the prime factorization of 54784 and 54800. After we will calculate the factors of 54784 and 54800 and find the biggest common factor number .

Step-1: Prime Factorization of 54784

Prime factors of 54784 are 2, 107. Prime factorization of 54784 in exponential form is:

54784 = 2⁹ × 107¹

Step-2: Prime Factorization of 54800

Prime factors of 54800 are 2, 5, 137. Prime factorization of 54800 in exponential form is:

54800 = 2⁴ × 5² × 137¹

Step-3: Factors of 54784

List of positive integer factors of 54784 that divides 54784 without a remainder.

1, 2, 4, 8, 16, 32, 64, 107, 128, 214, 256, 428, 512, 856, 1712, 3424, 6848, 13696, 27392

Step-4: Factors of 54800

List of positive integer factors of 54800 that divides 54784 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 137, 200, 274, 400, 548, 685, 1096, 1370, 2192, 2740, 3425, 5480, 6850, 10960, 13700, 27400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54784 and 54800. The biggest common factor number is the GCF number.
So the greatest common factor 54784 and 54800 is 16.

Also check out the Least Common Multiple of 54784 and 54800