What is the Greatest Common Factor of 38991 and 39000?

Greatest common factor (GCF) of 38991 and 39000 is 3.

GCF(38991,39000) = 3

We will now calculate the prime factors of 38991 and 39000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38991 and 39000.

How to find the GCF of 38991 and 39000?

We will first find the prime factorization of 38991 and 39000. After we will calculate the factors of 38991 and 39000 and find the biggest common factor number .

Step-1: Prime Factorization of 38991

Prime factors of 38991 are 3, 41, 317. Prime factorization of 38991 in exponential form is:

38991 = 3¹ × 41¹ × 317¹

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 38991

List of positive integer factors of 38991 that divides 38991 without a remainder.

1, 3, 41, 123, 317, 951, 12997

Step-4: Factors of 39000

List of positive integer factors of 39000 that divides 38991 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 38991 and 39000. The biggest common factor number is the GCF number.
So the greatest common factor 38991 and 39000 is 3.

Also check out the Least Common Multiple of 38991 and 39000