What is the Greatest Common Factor of 38985 and 39000?

Greatest common factor (GCF) of 38985 and 39000 is 15.

GCF(38985,39000) = 15

We will now calculate the prime factors of 38985 and 39000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38985 and 39000.

How to find the GCF of 38985 and 39000?

We will first find the prime factorization of 38985 and 39000. After we will calculate the factors of 38985 and 39000 and find the biggest common factor number .

Step-1: Prime Factorization of 38985

Prime factors of 38985 are 3, 5, 23, 113. Prime factorization of 38985 in exponential form is:

38985 = 3¹ × 5¹ × 23¹ × 113¹

Step-2: Prime Factorization of 39000

Prime factors of 39000 are 2, 3, 5, 13. Prime factorization of 39000 in exponential form is:

39000 = 2³ × 3¹ × 5³ × 13¹

Step-3: Factors of 38985

List of positive integer factors of 38985 that divides 38985 without a remainder.

1, 3, 5, 15, 23, 69, 113, 115, 339, 345, 565, 1695, 2599, 7797, 12995

Step-4: Factors of 39000

List of positive integer factors of 39000 that divides 38985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 25, 26, 30, 39, 40, 50, 52, 60, 65, 75, 78, 100, 104, 120, 125, 130, 150, 156, 195, 200, 250, 260, 300, 312, 325, 375, 390, 500, 520, 600, 650, 750, 780, 975, 1000, 1300, 1500, 1560, 1625, 1950, 2600, 3000, 3250, 3900, 4875, 6500, 7800, 9750, 13000, 19500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38985 and 39000. The biggest common factor number is the GCF number.
So the greatest common factor 38985 and 39000 is 15.

Also check out the Least Common Multiple of 38985 and 39000