What is the Greatest Common Factor of 81900 and 81918?

Greatest common factor (GCF) of 81900 and 81918 is 18.

GCF(81900,81918) = 18

We will now calculate the prime factors of 81900 and 81918, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81900 and 81918.

How to find the GCF of 81900 and 81918?

We will first find the prime factorization of 81900 and 81918. After we will calculate the factors of 81900 and 81918 and find the biggest common factor number .

Step-1: Prime Factorization of 81900

Prime factors of 81900 are 2, 3, 5, 7, 13. Prime factorization of 81900 in exponential form is:

81900 = 2² × 3² × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 81918

Prime factors of 81918 are 2, 3, 37, 41. Prime factorization of 81918 in exponential form is:

81918 = 2¹ × 3³ × 37¹ × 41¹

Step-3: Factors of 81900

List of positive integer factors of 81900 that divides 81900 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21, 25, 26, 28, 30, 35, 36, 39, 42, 45, 50, 52, 60, 63, 65, 70, 75, 78, 84, 90, 91, 100, 105, 117, 126, 130, 140, 150, 156, 175, 180, 182, 195, 210, 225, 234, 252, 260, 273, 300, 315, 325, 350, 364, 390, 420, 450, 455, 468, 525, 546, 585, 630, 650, 700, 780, 819, 900, 910, 975, 1050, 1092, 1170, 1260, 1300, 1365, 1575, 1638, 1820, 1950, 2100, 2275, 2340, 2730, 2925, 3150, 3276, 3900, 4095, 4550, 5460, 5850, 6300, 6825, 8190, 9100, 11700, 13650, 16380, 20475, 27300, 40950

Step-4: Factors of 81918

List of positive integer factors of 81918 that divides 81900 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 41, 54, 74, 82, 111, 123, 222, 246, 333, 369, 666, 738, 999, 1107, 1517, 1998, 2214, 3034, 4551, 9102, 13653, 27306, 40959

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81900 and 81918. The biggest common factor number is the GCF number.
So the greatest common factor 81900 and 81918 is 18.

Also check out the Least Common Multiple of 81900 and 81918