What is the Greatest Common Factor of 21249 and 21264?

Greatest common factor (GCF) of 21249 and 21264 is 3.

GCF(21249,21264) = 3

We will now calculate the prime factors of 21249 and 21264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21249 and 21264.

How to find the GCF of 21249 and 21264?

We will first find the prime factorization of 21249 and 21264. After we will calculate the factors of 21249 and 21264 and find the biggest common factor number .

Step-1: Prime Factorization of 21249

Prime factors of 21249 are 3, 787. Prime factorization of 21249 in exponential form is:

21249 = 3³ × 787¹

Step-2: Prime Factorization of 21264

Prime factors of 21264 are 2, 3, 443. Prime factorization of 21264 in exponential form is:

21264 = 2⁴ × 3¹ × 443¹

Step-3: Factors of 21249

List of positive integer factors of 21249 that divides 21249 without a remainder.

1, 3, 9, 27, 787, 2361, 7083

Step-4: Factors of 21264

List of positive integer factors of 21264 that divides 21249 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 443, 886, 1329, 1772, 2658, 3544, 5316, 7088, 10632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21249 and 21264. The biggest common factor number is the GCF number.
So the greatest common factor 21249 and 21264 is 3.

Also check out the Least Common Multiple of 21249 and 21264