What is the Greatest Common Factor of 51980 and 52000?

Greatest common factor (GCF) of 51980 and 52000 is 20.

GCF(51980,52000) = 20

We will now calculate the prime factors of 51980 and 52000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51980 and 52000.

How to find the GCF of 51980 and 52000?

We will first find the prime factorization of 51980 and 52000. After we will calculate the factors of 51980 and 52000 and find the biggest common factor number .

Step-1: Prime Factorization of 51980

Prime factors of 51980 are 2, 5, 23, 113. Prime factorization of 51980 in exponential form is:

51980 = 2² × 5¹ × 23¹ × 113¹

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 51980

List of positive integer factors of 51980 that divides 51980 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 113, 115, 226, 230, 452, 460, 565, 1130, 2260, 2599, 5198, 10396, 12995, 25990

Step-4: Factors of 52000

List of positive integer factors of 52000 that divides 51980 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 51980 and 52000. The biggest common factor number is the GCF number.
So the greatest common factor 51980 and 52000 is 20.

Also check out the Least Common Multiple of 51980 and 52000