What is the Greatest Common Factor of 21280 and 21300?

Greatest common factor (GCF) of 21280 and 21300 is 20.

GCF(21280,21300) = 20

We will now calculate the prime factors of 21280 and 21300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21280 and 21300.

How to find the GCF of 21280 and 21300?

We will first find the prime factorization of 21280 and 21300. After we will calculate the factors of 21280 and 21300 and find the biggest common factor number .

Step-1: Prime Factorization of 21280

Prime factors of 21280 are 2, 5, 7, 19. Prime factorization of 21280 in exponential form is:

21280 = 2⁵ × 5¹ × 7¹ × 19¹

Step-2: Prime Factorization of 21300

Prime factors of 21300 are 2, 3, 5, 71. Prime factorization of 21300 in exponential form is:

21300 = 2² × 3¹ × 5² × 71¹

Step-3: Factors of 21280

List of positive integer factors of 21280 that divides 21280 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 28, 32, 35, 38, 40, 56, 70, 76, 80, 95, 112, 133, 140, 152, 160, 190, 224, 266, 280, 304, 380, 532, 560, 608, 665, 760, 1064, 1120, 1330, 1520, 2128, 2660, 3040, 4256, 5320, 10640

Step-4: Factors of 21300

List of positive integer factors of 21300 that divides 21280 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 71, 75, 100, 142, 150, 213, 284, 300, 355, 426, 710, 852, 1065, 1420, 1775, 2130, 3550, 4260, 5325, 7100, 10650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21280 and 21300. The biggest common factor number is the GCF number.
So the greatest common factor 21280 and 21300 is 20.

Also check out the Least Common Multiple of 21280 and 21300