What is the Greatest Common Factor of 21409 and 21420?

Greatest common factor (GCF) of 21409 and 21420 is 1.

GCF(21409,21420) = 1

We will now calculate the prime factors of 21409 and 21420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21409 and 21420.

How to find the GCF of 21409 and 21420?

We will first find the prime factorization of 21409 and 21420. After we will calculate the factors of 21409 and 21420 and find the biggest common factor number .

Step-1: Prime Factorization of 21409

Prime factors of 21409 are 79, 271. Prime factorization of 21409 in exponential form is:

21409 = 79¹ × 271¹

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 21409

List of positive integer factors of 21409 that divides 21409 without a remainder.

1, 79, 271

Step-4: Factors of 21420

List of positive integer factors of 21420 that divides 21409 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 21409 and 21420. The biggest common factor number is the GCF number.
So the greatest common factor 21409 and 21420 is 1.

Also check out the Least Common Multiple of 21409 and 21420