What is the Greatest Common Factor of 39000 and 39005?

Greatest common factor (GCF) of 39000 and 39005 is 5.

GCF(39000,39005) = 5

We will now calculate the prime factors of 39000 and 39005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39000 and 39005.

How to find the GCF of 39000 and 39005?

We will first find the prime factorization of 39000 and 39005. After we will calculate the factors of 39000 and 39005 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39005

Prime factors of 39005 are 5, 29, 269. Prime factorization of 39005 in exponential form is:

39005 = 5¹ × 29¹ × 269¹

Step-3: Factors of 39000

List of positive integer factors of 39000 that divides 39000 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

Step-4: Factors of 39005

List of positive integer factors of 39005 that divides 39000 without a remainder.

1, 5, 29, 145, 269, 1345, 7801

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39000 and 39005. The biggest common factor number is the GCF number.
So the greatest common factor 39000 and 39005 is 5.

Also check out the Least Common Multiple of 39000 and 39005