What is the Greatest Common Factor of 85980 and 86000?

Greatest common factor (GCF) of 85980 and 86000 is 20.

GCF(85980,86000) = 20

We will now calculate the prime factors of 85980 and 86000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85980 and 86000.

How to find the GCF of 85980 and 86000?

We will first find the prime factorization of 85980 and 86000. After we will calculate the factors of 85980 and 86000 and find the biggest common factor number .

Step-1: Prime Factorization of 85980

Prime factors of 85980 are 2, 3, 5, 1433. Prime factorization of 85980 in exponential form is:

85980 = 2² × 3¹ × 5¹ × 1433¹

Step-2: Prime Factorization of 86000

Prime factors of 86000 are 2, 5, 43. Prime factorization of 86000 in exponential form is:

86000 = 2⁴ × 5³ × 43¹

Step-3: Factors of 85980

List of positive integer factors of 85980 that divides 85980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1433, 2866, 4299, 5732, 7165, 8598, 14330, 17196, 21495, 28660, 42990

Step-4: Factors of 86000

List of positive integer factors of 86000 that divides 85980 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 43, 50, 80, 86, 100, 125, 172, 200, 215, 250, 344, 400, 430, 500, 688, 860, 1000, 1075, 1720, 2000, 2150, 3440, 4300, 5375, 8600, 10750, 17200, 21500, 43000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85980 and 86000. The biggest common factor number is the GCF number.
So the greatest common factor 85980 and 86000 is 20.

Also check out the Least Common Multiple of 85980 and 86000