What is the Greatest Common Factor of 85988 and 86000?

Greatest common factor (GCF) of 85988 and 86000 is 4.

GCF(85988,86000) = 4

We will now calculate the prime factors of 85988 and 86000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85988 and 86000.

How to find the GCF of 85988 and 86000?

We will first find the prime factorization of 85988 and 86000. After we will calculate the factors of 85988 and 86000 and find the biggest common factor number .

Step-1: Prime Factorization of 85988

Prime factors of 85988 are 2, 7, 37, 83. Prime factorization of 85988 in exponential form is:

85988 = 2² × 7¹ × 37¹ × 83¹

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 85988

List of positive integer factors of 85988 that divides 85988 without a remainder.

1, 2, 4, 7, 14, 28, 37, 74, 83, 148, 166, 259, 332, 518, 581, 1036, 1162, 2324, 3071, 6142, 12284, 21497, 42994

Step-4: Factors of 86000

List of positive integer factors of 86000 that divides 85988 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 85988 and 86000. The biggest common factor number is the GCF number.
So the greatest common factor 85988 and 86000 is 4.

Also check out the Least Common Multiple of 85988 and 86000