What is the Greatest Common Factor of 21120 and 21140?

Greatest common factor (GCF) of 21120 and 21140 is 20.

GCF(21120,21140) = 20

We will now calculate the prime factors of 21120 and 21140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21120 and 21140.

How to find the GCF of 21120 and 21140?

We will first find the prime factorization of 21120 and 21140. After we will calculate the factors of 21120 and 21140 and find the biggest common factor number .

Step-1: Prime Factorization of 21120

Prime factors of 21120 are 2, 3, 5, 11. Prime factorization of 21120 in exponential form is:

21120 = 2⁷ × 3¹ × 5¹ × 11¹

Step-2: Prime Factorization of 21140

Prime factors of 21140 are 2, 5, 7, 151. Prime factorization of 21140 in exponential form is:

21140 = 2² × 5¹ × 7¹ × 151¹

Step-3: Factors of 21120

List of positive integer factors of 21120 that divides 21120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240, 264, 320, 330, 352, 384, 440, 480, 528, 640, 660, 704, 880, 960, 1056, 1320, 1408, 1760, 1920, 2112, 2640, 3520, 4224, 5280, 7040, 10560

Step-4: Factors of 21140

List of positive integer factors of 21140 that divides 21120 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 151, 302, 604, 755, 1057, 1510, 2114, 3020, 4228, 5285, 10570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21120 and 21140. The biggest common factor number is the GCF number.
So the greatest common factor 21120 and 21140 is 20.

Also check out the Least Common Multiple of 21120 and 21140