What is the Greatest Common Factor of 39000 and 39009?

Greatest common factor (GCF) of 39000 and 39009 is 3.

GCF(39000,39009) = 3

We will now calculate the prime factors of 39000 and 39009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39000 and 39009.

How to find the GCF of 39000 and 39009?

We will first find the prime factorization of 39000 and 39009. After we will calculate the factors of 39000 and 39009 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 39009

Prime factors of 39009 are 3, 13003. Prime factorization of 39009 in exponential form is:

39009 = 3¹ × 13003¹

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 39009

List of positive integer factors of 39009 that divides 39000 without a remainder.

1, 3, 13003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39000 and 39009. The biggest common factor number is the GCF number.
So the greatest common factor 39000 and 39009 is 3.

Also check out the Least Common Multiple of 39000 and 39009