What is the Greatest Common Factor of 57980 and 58000?

Greatest common factor (GCF) of 57980 and 58000 is 20.

GCF(57980,58000) = 20

We will now calculate the prime factors of 57980 and 58000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57980 and 58000.

How to find the GCF of 57980 and 58000?

We will first find the prime factorization of 57980 and 58000. After we will calculate the factors of 57980 and 58000 and find the biggest common factor number .

Step-1: Prime Factorization of 57980

Prime factors of 57980 are 2, 5, 13, 223. Prime factorization of 57980 in exponential form is:

57980 = 2² × 5¹ × 13¹ × 223¹

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 57980

List of positive integer factors of 57980 that divides 57980 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 223, 260, 446, 892, 1115, 2230, 2899, 4460, 5798, 11596, 14495, 28990

Step-4: Factors of 58000

List of positive integer factors of 58000 that divides 57980 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 57980 and 58000. The biggest common factor number is the GCF number.
So the greatest common factor 57980 and 58000 is 20.

Also check out the Least Common Multiple of 57980 and 58000