What is the Greatest Common Factor of 51988 and 52000?

Greatest common factor (GCF) of 51988 and 52000 is 4.

GCF(51988,52000) = 4

We will now calculate the prime factors of 51988 and 52000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51988 and 52000.

How to find the GCF of 51988 and 52000?

We will first find the prime factorization of 51988 and 52000. After we will calculate the factors of 51988 and 52000 and find the biggest common factor number .

Step-1: Prime Factorization of 51988

Prime factors of 51988 are 2, 41, 317. Prime factorization of 51988 in exponential form is:

51988 = 2² × 41¹ × 317¹

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 51988

List of positive integer factors of 51988 that divides 51988 without a remainder.

1, 2, 4, 41, 82, 164, 317, 634, 1268, 12997, 25994

Step-4: Factors of 52000

List of positive integer factors of 52000 that divides 51988 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 51988 and 52000. The biggest common factor number is the GCF number.
So the greatest common factor 51988 and 52000 is 4.

Also check out the Least Common Multiple of 51988 and 52000