What is the Greatest Common Factor of 21504 and 21520?

Greatest common factor (GCF) of 21504 and 21520 is 16.

GCF(21504,21520) = 16

We will now calculate the prime factors of 21504 and 21520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21504 and 21520.

How to find the GCF of 21504 and 21520?

We will first find the prime factorization of 21504 and 21520. After we will calculate the factors of 21504 and 21520 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 21520

Prime factors of 21520 are 2, 5, 269. Prime factorization of 21520 in exponential form is:

21520 = 2⁴ × 5¹ × 269¹

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 21520

List of positive integer factors of 21520 that divides 21504 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 269, 538, 1076, 1345, 2152, 2690, 4304, 5380, 10760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21504 and 21520. The biggest common factor number is the GCF number.
So the greatest common factor 21504 and 21520 is 16.

Also check out the Least Common Multiple of 21504 and 21520