What is the Greatest Common Factor of 21509 and 21528?

Greatest common factor (GCF) of 21509 and 21528 is 1.

GCF(21509,21528) = 1

We will now calculate the prime factors of 21509 and 21528, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21509 and 21528.

How to find the GCF of 21509 and 21528?

We will first find the prime factorization of 21509 and 21528. After we will calculate the factors of 21509 and 21528 and find the biggest common factor number .

Step-1: Prime Factorization of 21509

Prime factors of 21509 are 137, 157. Prime factorization of 21509 in exponential form is:

21509 = 137¹ × 157¹

Step-2: Prime Factorization of 21528

Prime factors of 21528 are 2, 3, 13, 23. Prime factorization of 21528 in exponential form is:

21528 = 2³ × 3² × 13¹ × 23¹

Step-3: Factors of 21509

List of positive integer factors of 21509 that divides 21509 without a remainder.

1, 137, 157

Step-4: Factors of 21528

List of positive integer factors of 21528 that divides 21509 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 23, 24, 26, 36, 39, 46, 52, 69, 72, 78, 92, 104, 117, 138, 156, 184, 207, 234, 276, 299, 312, 414, 468, 552, 598, 828, 897, 936, 1196, 1656, 1794, 2392, 2691, 3588, 5382, 7176, 10764

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21509 and 21528. The biggest common factor number is the GCF number.
So the greatest common factor 21509 and 21528 is 1.

Also check out the Least Common Multiple of 21509 and 21528