What is the Greatest Common Factor of 21406 and 21420?

Greatest common factor (GCF) of 21406 and 21420 is 14.

GCF(21406,21420) = 14

We will now calculate the prime factors of 21406 and 21420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21406 and 21420.

How to find the GCF of 21406 and 21420?

We will first find the prime factorization of 21406 and 21420. After we will calculate the factors of 21406 and 21420 and find the biggest common factor number .

Step-1: Prime Factorization of 21406

Prime factors of 21406 are 2, 7, 11, 139. Prime factorization of 21406 in exponential form is:

21406 = 2¹ × 7¹ × 11¹ × 139¹

Step-2: 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-3: Factors of 21406

List of positive integer factors of 21406 that divides 21406 without a remainder.

1, 2, 7, 11, 14, 22, 77, 139, 154, 278, 973, 1529, 1946, 3058, 10703

Step-4: Factors of 21420

List of positive integer factors of 21420 that divides 21406 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21406 and 21420. The biggest common factor number is the GCF number.
So the greatest common factor 21406 and 21420 is 14.

Also check out the Least Common Multiple of 21406 and 21420