What is the Greatest Common Factor of 81888 and 81900?

Greatest common factor (GCF) of 81888 and 81900 is 12.

GCF(81888,81900) = 12

We will now calculate the prime factors of 81888 and 81900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81888 and 81900.

How to find the GCF of 81888 and 81900?

We will first find the prime factorization of 81888 and 81900. After we will calculate the factors of 81888 and 81900 and find the biggest common factor number .

Step-1: Prime Factorization of 81888

Prime factors of 81888 are 2, 3, 853. Prime factorization of 81888 in exponential form is:

81888 = 2⁵ × 3¹ × 853¹

Step-2: 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-3: Factors of 81888

List of positive integer factors of 81888 that divides 81888 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 853, 1706, 2559, 3412, 5118, 6824, 10236, 13648, 20472, 27296, 40944

Step-4: Factors of 81900

List of positive integer factors of 81900 that divides 81888 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81888 and 81900. The biggest common factor number is the GCF number.
So the greatest common factor 81888 and 81900 is 12.

Also check out the Least Common Multiple of 81888 and 81900