What is the Greatest Common Factor of 81984 and 82000?

Greatest common factor (GCF) of 81984 and 82000 is 16.

GCF(81984,82000) = 16

We will now calculate the prime factors of 81984 and 82000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81984 and 82000.

How to find the GCF of 81984 and 82000?

We will first find the prime factorization of 81984 and 82000. After we will calculate the factors of 81984 and 82000 and find the biggest common factor number .

Step-1: Prime Factorization of 81984

Prime factors of 81984 are 2, 3, 7, 61. Prime factorization of 81984 in exponential form is:

81984 = 2⁶ × 3¹ × 7¹ × 61¹

Step-2: Prime Factorization of 82000

Prime factors of 82000 are 2, 5, 41. Prime factorization of 82000 in exponential form is:

82000 = 2⁴ × 5³ × 41¹

Step-3: Factors of 81984

List of positive integer factors of 81984 that divides 81984 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 61, 64, 84, 96, 112, 122, 168, 183, 192, 224, 244, 336, 366, 427, 448, 488, 672, 732, 854, 976, 1281, 1344, 1464, 1708, 1952, 2562, 2928, 3416, 3904, 5124, 5856, 6832, 10248, 11712, 13664, 20496, 27328, 40992

Step-4: Factors of 82000

List of positive integer factors of 82000 that divides 81984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 125, 164, 200, 205, 250, 328, 400, 410, 500, 656, 820, 1000, 1025, 1640, 2000, 2050, 3280, 4100, 5125, 8200, 10250, 16400, 20500, 41000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81984 and 82000. The biggest common factor number is the GCF number.
So the greatest common factor 81984 and 82000 is 16.

Also check out the Least Common Multiple of 81984 and 82000