What is the Greatest Common Factor of 33984 and 34000?

Greatest common factor (GCF) of 33984 and 34000 is 16.

GCF(33984,34000) = 16

We will now calculate the prime factors of 33984 and 34000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33984 and 34000.

How to find the GCF of 33984 and 34000?

We will first find the prime factorization of 33984 and 34000. After we will calculate the factors of 33984 and 34000 and find the biggest common factor number .

Step-1: Prime Factorization of 33984

Prime factors of 33984 are 2, 3, 59. Prime factorization of 33984 in exponential form is:

33984 = 2⁶ × 3² × 59¹

Step-2: Prime Factorization of 34000

Prime factors of 34000 are 2, 5, 17. Prime factorization of 34000 in exponential form is:

34000 = 2⁴ × 5³ × 17¹

Step-3: Factors of 33984

List of positive integer factors of 33984 that divides 33984 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64, 72, 96, 118, 144, 177, 192, 236, 288, 354, 472, 531, 576, 708, 944, 1062, 1416, 1888, 2124, 2832, 3776, 4248, 5664, 8496, 11328, 16992

Step-4: Factors of 34000

List of positive integer factors of 34000 that divides 33984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33984 and 34000. The biggest common factor number is the GCF number.
So the greatest common factor 33984 and 34000 is 16.

Also check out the Least Common Multiple of 33984 and 34000