What is the Greatest Common Factor of 21564 and 21584?

Greatest common factor (GCF) of 21564 and 21584 is 4.

GCF(21564,21584) = 4

We will now calculate the prime factors of 21564 and 21584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21564 and 21584.

How to find the GCF of 21564 and 21584?

We will first find the prime factorization of 21564 and 21584. After we will calculate the factors of 21564 and 21584 and find the biggest common factor number .

Step-1: Prime Factorization of 21564

Prime factors of 21564 are 2, 3, 599. Prime factorization of 21564 in exponential form is:

21564 = 2² × 3² × 599¹

Step-2: Prime Factorization of 21584

Prime factors of 21584 are 2, 19, 71. Prime factorization of 21584 in exponential form is:

21584 = 2⁴ × 19¹ × 71¹

Step-3: Factors of 21564

List of positive integer factors of 21564 that divides 21564 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 599, 1198, 1797, 2396, 3594, 5391, 7188, 10782

Step-4: Factors of 21584

List of positive integer factors of 21584 that divides 21564 without a remainder.

1, 2, 4, 8, 16, 19, 38, 71, 76, 142, 152, 284, 304, 568, 1136, 1349, 2698, 5396, 10792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21564 and 21584. The biggest common factor number is the GCF number.
So the greatest common factor 21564 and 21584 is 4.

Also check out the Least Common Multiple of 21564 and 21584