What is the Greatest Common Factor of 86980 and 87000?

Greatest common factor (GCF) of 86980 and 87000 is 20.

GCF(86980,87000) = 20

We will now calculate the prime factors of 86980 and 87000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 86980 and 87000.

How to find the GCF of 86980 and 87000?

We will first find the prime factorization of 86980 and 87000. After we will calculate the factors of 86980 and 87000 and find the biggest common factor number .

Step-1: Prime Factorization of 86980

Prime factors of 86980 are 2, 5, 4349. Prime factorization of 86980 in exponential form is:

86980 = 2² × 5¹ × 4349¹

Step-2: Prime Factorization of 87000

Prime factors of 87000 are 2, 3, 5, 29. Prime factorization of 87000 in exponential form is:

87000 = 2³ × 3¹ × 5³ × 29¹

Step-3: Factors of 86980

List of positive integer factors of 86980 that divides 86980 without a remainder.

1, 2, 4, 5, 10, 20, 4349, 8698, 17396, 21745, 43490

Step-4: Factors of 87000

List of positive integer factors of 87000 that divides 86980 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 29, 30, 40, 50, 58, 60, 75, 87, 100, 116, 120, 125, 145, 150, 174, 200, 232, 250, 290, 300, 348, 375, 435, 500, 580, 600, 696, 725, 750, 870, 1000, 1160, 1450, 1500, 1740, 2175, 2900, 3000, 3480, 3625, 4350, 5800, 7250, 8700, 10875, 14500, 17400, 21750, 29000, 43500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 86980 and 87000. The biggest common factor number is the GCF number.
So the greatest common factor 86980 and 87000 is 20.

Also check out the Least Common Multiple of 86980 and 87000