What is the Greatest Common Factor of 21564 and 21574?

Greatest common factor (GCF) of 21564 and 21574 is 2.

GCF(21564,21574) = 2

We will now calculate the prime factors of 21564 and 21574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21564 and 21574.

How to find the GCF of 21564 and 21574?

We will first find the prime factorization of 21564 and 21574. After we will calculate the factors of 21564 and 21574 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 21574

Prime factors of 21574 are 2, 7, 23, 67. Prime factorization of 21574 in exponential form is:

21574 = 2¹ × 7¹ × 23¹ × 67¹

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 21574

List of positive integer factors of 21574 that divides 21564 without a remainder.

1, 2, 7, 14, 23, 46, 67, 134, 161, 322, 469, 938, 1541, 3082, 10787

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21564 and 21574. The biggest common factor number is the GCF number.
So the greatest common factor 21564 and 21574 is 2.

Also check out the Least Common Multiple of 21564 and 21574