What is the Greatest Common Factor of 21500 and 21504?

Greatest common factor (GCF) of 21500 and 21504 is 4.

GCF(21500,21504) = 4

We will now calculate the prime factors of 21500 and 21504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21500 and 21504.

How to find the GCF of 21500 and 21504?

We will first find the prime factorization of 21500 and 21504. After we will calculate the factors of 21500 and 21504 and find the biggest common factor number .

Step-1: Prime Factorization of 21500

Prime factors of 21500 are 2, 5, 43. Prime factorization of 21500 in exponential form is:

21500 = 2² × 5³ × 43¹

Step-2: 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-3: Factors of 21500

List of positive integer factors of 21500 that divides 21500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 43, 50, 86, 100, 125, 172, 215, 250, 430, 500, 860, 1075, 2150, 4300, 5375, 10750

Step-4: Factors of 21504

List of positive integer factors of 21504 that divides 21500 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21500 and 21504. The biggest common factor number is the GCF number.
So the greatest common factor 21500 and 21504 is 4.

Also check out the Least Common Multiple of 21500 and 21504