What is the Greatest Common Factor of 21825 and 21840?

Greatest common factor (GCF) of 21825 and 21840 is 15.

GCF(21825,21840) = 15

We will now calculate the prime factors of 21825 and 21840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21825 and 21840.

How to find the GCF of 21825 and 21840?

We will first find the prime factorization of 21825 and 21840. After we will calculate the factors of 21825 and 21840 and find the biggest common factor number .

Step-1: Prime Factorization of 21825

Prime factors of 21825 are 3, 5, 97. Prime factorization of 21825 in exponential form is:

21825 = 3² × 5² × 97¹

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 21825

List of positive integer factors of 21825 that divides 21825 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 97, 225, 291, 485, 873, 1455, 2425, 4365, 7275

Step-4: Factors of 21840

List of positive integer factors of 21840 that divides 21825 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 21825 and 21840. The biggest common factor number is the GCF number.
So the greatest common factor 21825 and 21840 is 15.

Also check out the Least Common Multiple of 21825 and 21840