What is the Greatest Common Factor of 55980 and 56000?

Greatest common factor (GCF) of 55980 and 56000 is 20.

GCF(55980,56000) = 20

We will now calculate the prime factors of 55980 and 56000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55980 and 56000.

How to find the GCF of 55980 and 56000?

We will first find the prime factorization of 55980 and 56000. After we will calculate the factors of 55980 and 56000 and find the biggest common factor number .

Step-1: Prime Factorization of 55980

Prime factors of 55980 are 2, 3, 5, 311. Prime factorization of 55980 in exponential form is:

55980 = 2² × 3² × 5¹ × 311¹

Step-2: Prime Factorization of 56000

Prime factors of 56000 are 2, 5, 7. Prime factorization of 56000 in exponential form is:

56000 = 2⁶ × 5³ × 7¹

Step-3: Factors of 55980

List of positive integer factors of 55980 that divides 55980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 311, 622, 933, 1244, 1555, 1866, 2799, 3110, 3732, 4665, 5598, 6220, 9330, 11196, 13995, 18660, 27990

Step-4: Factors of 56000

List of positive integer factors of 56000 that divides 55980 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 125, 140, 160, 175, 200, 224, 250, 280, 320, 350, 400, 448, 500, 560, 700, 800, 875, 1000, 1120, 1400, 1600, 1750, 2000, 2240, 2800, 3500, 4000, 5600, 7000, 8000, 11200, 14000, 28000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55980 and 56000. The biggest common factor number is the GCF number.
So the greatest common factor 55980 and 56000 is 20.

Also check out the Least Common Multiple of 55980 and 56000