What is the Greatest Common Factor of 21827 and 21840?

Greatest common factor (GCF) of 21827 and 21840 is 13.

GCF(21827,21840) = 13

We will now calculate the prime factors of 21827 and 21840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21827 and 21840.

How to find the GCF of 21827 and 21840?

We will first find the prime factorization of 21827 and 21840. After we will calculate the factors of 21827 and 21840 and find the biggest common factor number .

Step-1: Prime Factorization of 21827

Prime factors of 21827 are 13, 23, 73. Prime factorization of 21827 in exponential form is:

21827 = 13¹ × 23¹ × 73¹

Step-2: 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-3: Factors of 21827

List of positive integer factors of 21827 that divides 21827 without a remainder.

1, 13, 23, 73, 299, 949, 1679

Step-4: Factors of 21840

List of positive integer factors of 21840 that divides 21827 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21827 and 21840. The biggest common factor number is the GCF number.
So the greatest common factor 21827 and 21840 is 13.

Also check out the Least Common Multiple of 21827 and 21840