What is the Greatest Common Factor of 21552 and 21564?

Greatest common factor (GCF) of 21552 and 21564 is 12.

GCF(21552,21564) = 12

We will now calculate the prime factors of 21552 and 21564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21552 and 21564.

How to find the GCF of 21552 and 21564?

We will first find the prime factorization of 21552 and 21564. After we will calculate the factors of 21552 and 21564 and find the biggest common factor number .

Step-1: Prime Factorization of 21552

Prime factors of 21552 are 2, 3, 449. Prime factorization of 21552 in exponential form is:

21552 = 2⁴ × 3¹ × 449¹

Step-2: 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-3: Factors of 21552

List of positive integer factors of 21552 that divides 21552 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 449, 898, 1347, 1796, 2694, 3592, 5388, 7184, 10776

Step-4: Factors of 21564

List of positive integer factors of 21564 that divides 21552 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21552 and 21564. The biggest common factor number is the GCF number.
So the greatest common factor 21552 and 21564 is 12.

Also check out the Least Common Multiple of 21552 and 21564