What is the Greatest Common Factor of 10980 and 11000?

Greatest common factor (GCF) of 10980 and 11000 is 20.

GCF(10980,11000) = 20

We will now calculate the prime factors of 10980 and 11000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10980 and 11000.

How to find the GCF of 10980 and 11000?

We will first find the prime factorization of 10980 and 11000. After we will calculate the factors of 10980 and 11000 and find the biggest common factor number .

Step-1: Prime Factorization of 10980

Prime factors of 10980 are 2, 3, 5, 61. Prime factorization of 10980 in exponential form is:

10980 = 2² × 3² × 5¹ × 61¹

Step-2: Prime Factorization of 11000

Prime factors of 11000 are 2, 5, 11. Prime factorization of 11000 in exponential form is:

11000 = 2³ × 5³ × 11¹

Step-3: Factors of 10980

List of positive integer factors of 10980 that divides 10980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 61, 90, 122, 180, 183, 244, 305, 366, 549, 610, 732, 915, 1098, 1220, 1830, 2196, 2745, 3660, 5490

Step-4: Factors of 11000

List of positive integer factors of 11000 that divides 10980 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 125, 200, 220, 250, 275, 440, 500, 550, 1000, 1100, 1375, 2200, 2750, 5500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10980 and 11000. The biggest common factor number is the GCF number.
So the greatest common factor 10980 and 11000 is 20.

Also check out the Least Common Multiple of 10980 and 11000