What is the Greatest Common Factor of 39984 and 40000?

Greatest common factor (GCF) of 39984 and 40000 is 16.

GCF(39984,40000) = 16

We will now calculate the prime factors of 39984 and 40000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39984 and 40000.

How to find the GCF of 39984 and 40000?

We will first find the prime factorization of 39984 and 40000. After we will calculate the factors of 39984 and 40000 and find the biggest common factor number .

Step-1: Prime Factorization of 39984

Prime factors of 39984 are 2, 3, 7, 17. Prime factorization of 39984 in exponential form is:

39984 = 2⁴ × 3¹ × 7² × 17¹

Step-2: Prime Factorization of 40000

Prime factors of 40000 are 2, 5. Prime factorization of 40000 in exponential form is:

40000 = 2⁶ × 5⁴

Step-3: Factors of 39984

List of positive integer factors of 39984 that divides 39984 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42, 48, 49, 51, 56, 68, 84, 98, 102, 112, 119, 136, 147, 168, 196, 204, 238, 272, 294, 336, 357, 392, 408, 476, 588, 714, 784, 816, 833, 952, 1176, 1428, 1666, 1904, 2352, 2499, 2856, 3332, 4998, 5712, 6664, 9996, 13328, 19992

Step-4: Factors of 40000

List of positive integer factors of 40000 that divides 39984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 1250, 1600, 2000, 2500, 4000, 5000, 8000, 10000, 20000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39984 and 40000. The biggest common factor number is the GCF number.
So the greatest common factor 39984 and 40000 is 16.

Also check out the Least Common Multiple of 39984 and 40000