What is the Greatest Common Factor of 21504 and 21512?

Greatest common factor (GCF) of 21504 and 21512 is 8.

GCF(21504,21512) = 8

We will now calculate the prime factors of 21504 and 21512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21504 and 21512.

How to find the GCF of 21504 and 21512?

We will first find the prime factorization of 21504 and 21512. After we will calculate the factors of 21504 and 21512 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 21512

Prime factors of 21512 are 2, 2689. Prime factorization of 21512 in exponential form is:

21512 = 2³ × 2689¹

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 21512

List of positive integer factors of 21512 that divides 21504 without a remainder.

1, 2, 4, 8, 2689, 5378, 10756

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21504 and 21512. The biggest common factor number is the GCF number.
So the greatest common factor 21504 and 21512 is 8.

Also check out the Least Common Multiple of 21504 and 21512