What is the Greatest Common Factor of 21504 and 21518?

Greatest common factor (GCF) of 21504 and 21518 is 14.

GCF(21504,21518) = 14

We will now calculate the prime factors of 21504 and 21518, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21504 and 21518.

How to find the GCF of 21504 and 21518?

We will first find the prime factorization of 21504 and 21518. After we will calculate the factors of 21504 and 21518 and find the biggest common factor number .

Step-1: Prime Factorization of 21504

Prime factors of 21504 are 2, 3, 7. Prime factorization of 21504 in exponential form is:

21504 = 2¹⁰ × 3¹ × 7¹

Step-2: Prime Factorization of 21518

Prime factors of 21518 are 2, 7, 29, 53. Prime factorization of 21518 in exponential form is:

21518 = 2¹ × 7¹ × 29¹ × 53¹

Step-3: Factors of 21504

List of positive integer factors of 21504 that divides 21504 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 512, 672, 768, 896, 1024, 1344, 1536, 1792, 2688, 3072, 3584, 5376, 7168, 10752

Step-4: Factors of 21518

List of positive integer factors of 21518 that divides 21504 without a remainder.

1, 2, 7, 14, 29, 53, 58, 106, 203, 371, 406, 742, 1537, 3074, 10759

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21504 and 21518. The biggest common factor number is the GCF number.
So the greatest common factor 21504 and 21518 is 14.

Also check out the Least Common Multiple of 21504 and 21518