What is the Greatest Common Factor of 21420 and 21440?

Greatest common factor (GCF) of 21420 and 21440 is 20.

GCF(21420,21440) = 20

We will now calculate the prime factors of 21420 and 21440, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21420 and 21440.

How to find the GCF of 21420 and 21440?

We will first find the prime factorization of 21420 and 21440. After we will calculate the factors of 21420 and 21440 and find the biggest common factor number .

Step-1: Prime Factorization of 21420

Prime factors of 21420 are 2, 3, 5, 7, 17. Prime factorization of 21420 in exponential form is:

21420 = 2² × 3² × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 21440

Prime factors of 21440 are 2, 5, 67. Prime factorization of 21440 in exponential form is:

21440 = 2⁶ × 5¹ × 67¹

Step-3: Factors of 21420

List of positive integer factors of 21420 that divides 21420 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 28, 30, 34, 35, 36, 42, 45, 51, 60, 63, 68, 70, 84, 85, 90, 102, 105, 119, 126, 140, 153, 170, 180, 204, 210, 238, 252, 255, 306, 315, 340, 357, 420, 476, 510, 595, 612, 630, 714, 765, 1020, 1071, 1190, 1260, 1428, 1530, 1785, 2142, 2380, 3060, 3570, 4284, 5355, 7140, 10710

Step-4: Factors of 21440

List of positive integer factors of 21440 that divides 21420 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 67, 80, 134, 160, 268, 320, 335, 536, 670, 1072, 1340, 2144, 2680, 4288, 5360, 10720

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21420 and 21440. The biggest common factor number is the GCF number.
So the greatest common factor 21420 and 21440 is 20.

Also check out the Least Common Multiple of 21420 and 21440