What is the Greatest Common Factor of 57982 and 58000?

Greatest common factor (GCF) of 57982 and 58000 is 2.

GCF(57982,58000) = 2

We will now calculate the prime factors of 57982 and 58000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57982 and 58000.

How to find the GCF of 57982 and 58000?

We will first find the prime factorization of 57982 and 58000. After we will calculate the factors of 57982 and 58000 and find the biggest common factor number .

Step-1: Prime Factorization of 57982

Prime factors of 57982 are 2, 53, 547. Prime factorization of 57982 in exponential form is:

57982 = 2¹ × 53¹ × 547¹

Step-2: Prime Factorization of 58000

Prime factors of 58000 are 2, 5, 29. Prime factorization of 58000 in exponential form is:

58000 = 2⁴ × 5³ × 29¹

Step-3: Factors of 57982

List of positive integer factors of 57982 that divides 57982 without a remainder.

1, 2, 53, 106, 547, 1094, 28991

Step-4: Factors of 58000

List of positive integer factors of 58000 that divides 57982 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 40, 50, 58, 80, 100, 116, 125, 145, 200, 232, 250, 290, 400, 464, 500, 580, 725, 1000, 1160, 1450, 2000, 2320, 2900, 3625, 5800, 7250, 11600, 14500, 29000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57982 and 58000. The biggest common factor number is the GCF number.
So the greatest common factor 57982 and 58000 is 2.

Also check out the Least Common Multiple of 57982 and 58000