What is the Greatest Common Factor of 51984 and 52000?

Greatest common factor (GCF) of 51984 and 52000 is 16.

GCF(51984,52000) = 16

We will now calculate the prime factors of 51984 and 52000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51984 and 52000.

How to find the GCF of 51984 and 52000?

We will first find the prime factorization of 51984 and 52000. After we will calculate the factors of 51984 and 52000 and find the biggest common factor number .

Step-1: Prime Factorization of 51984

Prime factors of 51984 are 2, 3, 19. Prime factorization of 51984 in exponential form is:

51984 = 2⁴ × 3² × 19²

Step-2: Prime Factorization of 52000

Prime factors of 52000 are 2, 5, 13. Prime factorization of 52000 in exponential form is:

52000 = 2⁵ × 5³ × 13¹

Step-3: Factors of 51984

List of positive integer factors of 51984 that divides 51984 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 36, 38, 48, 57, 72, 76, 114, 144, 152, 171, 228, 304, 342, 361, 456, 684, 722, 912, 1083, 1368, 1444, 2166, 2736, 2888, 3249, 4332, 5776, 6498, 8664, 12996, 17328, 25992

Step-4: Factors of 52000

List of positive integer factors of 52000 that divides 51984 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 125, 130, 160, 200, 208, 250, 260, 325, 400, 416, 500, 520, 650, 800, 1000, 1040, 1300, 1625, 2000, 2080, 2600, 3250, 4000, 5200, 6500, 10400, 13000, 26000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51984 and 52000. The biggest common factor number is the GCF number.
So the greatest common factor 51984 and 52000 is 16.

Also check out the Least Common Multiple of 51984 and 52000