What is the Greatest Common Factor of 21936 and 21945?

Greatest common factor (GCF) of 21936 and 21945 is 3.

GCF(21936,21945) = 3

We will now calculate the prime factors of 21936 and 21945, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21936 and 21945.

How to find the GCF of 21936 and 21945?

We will first find the prime factorization of 21936 and 21945. After we will calculate the factors of 21936 and 21945 and find the biggest common factor number .

Step-1: Prime Factorization of 21936

Prime factors of 21936 are 2, 3, 457. Prime factorization of 21936 in exponential form is:

21936 = 2⁴ × 3¹ × 457¹

Step-2: Prime Factorization of 21945

Prime factors of 21945 are 3, 5, 7, 11, 19. Prime factorization of 21945 in exponential form is:

21945 = 3¹ × 5¹ × 7¹ × 11¹ × 19¹

Step-3: Factors of 21936

List of positive integer factors of 21936 that divides 21936 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 457, 914, 1371, 1828, 2742, 3656, 5484, 7312, 10968

Step-4: Factors of 21945

List of positive integer factors of 21945 that divides 21936 without a remainder.

1, 3, 5, 7, 11, 15, 19, 21, 33, 35, 55, 57, 77, 95, 105, 133, 165, 209, 231, 285, 385, 399, 627, 665, 1045, 1155, 1463, 1995, 3135, 4389, 7315

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21936 and 21945. The biggest common factor number is the GCF number.
So the greatest common factor 21936 and 21945 is 3.

Also check out the Least Common Multiple of 21936 and 21945