What is the Greatest Common Factor of 81900 and 81914?

Greatest common factor (GCF) of 81900 and 81914 is 14.

GCF(81900,81914) = 14

We will now calculate the prime factors of 81900 and 81914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81900 and 81914.

How to find the GCF of 81900 and 81914?

We will first find the prime factorization of 81900 and 81914. After we will calculate the factors of 81900 and 81914 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 81914

Prime factors of 81914 are 2, 7, 5851. Prime factorization of 81914 in exponential form is:

81914 = 2¹ × 7¹ × 5851¹

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 81914

List of positive integer factors of 81914 that divides 81900 without a remainder.

1, 2, 7, 14, 5851, 11702, 40957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81900 and 81914. The biggest common factor number is the GCF number.
So the greatest common factor 81900 and 81914 is 14.

Also check out the Least Common Multiple of 81900 and 81914