What is the Greatest Common Factor of 21840 and 21856?

Greatest common factor (GCF) of 21840 and 21856 is 16.

GCF(21840,21856) = 16

We will now calculate the prime factors of 21840 and 21856, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21840 and 21856.

How to find the GCF of 21840 and 21856?

We will first find the prime factorization of 21840 and 21856. After we will calculate the factors of 21840 and 21856 and find the biggest common factor number .

Step-1: Prime Factorization of 21840

Prime factors of 21840 are 2, 3, 5, 7, 13. Prime factorization of 21840 in exponential form is:

21840 = 2⁴ × 3¹ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 21856

Prime factors of 21856 are 2, 683. Prime factorization of 21856 in exponential form is:

21856 = 2⁵ × 683¹

Step-3: Factors of 21840

List of positive integer factors of 21840 that divides 21840 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21, 24, 26, 28, 30, 35, 39, 40, 42, 48, 52, 56, 60, 65, 70, 78, 80, 84, 91, 104, 105, 112, 120, 130, 140, 156, 168, 182, 195, 208, 210, 240, 260, 273, 280, 312, 336, 364, 390, 420, 455, 520, 546, 560, 624, 728, 780, 840, 910, 1040, 1092, 1365, 1456, 1560, 1680, 1820, 2184, 2730, 3120, 3640, 4368, 5460, 7280, 10920

Step-4: Factors of 21856

List of positive integer factors of 21856 that divides 21840 without a remainder.

1, 2, 4, 8, 16, 32, 683, 1366, 2732, 5464, 10928

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21840 and 21856. The biggest common factor number is the GCF number.
So the greatest common factor 21840 and 21856 is 16.

Also check out the Least Common Multiple of 21840 and 21856