What is the Greatest Common Factor of 39000 and 39014?

Greatest common factor (GCF) of 39000 and 39014 is 2.

GCF(39000,39014) = 2

We will now calculate the prime factors of 39000 and 39014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39000 and 39014.

How to find the GCF of 39000 and 39014?

We will first find the prime factorization of 39000 and 39014. After we will calculate the factors of 39000 and 39014 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 39014

Prime factors of 39014 are 2, 19507. Prime factorization of 39014 in exponential form is:

39014 = 2¹ × 19507¹

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 39014

List of positive integer factors of 39014 that divides 39000 without a remainder.

1, 2, 19507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39000 and 39014. The biggest common factor number is the GCF number.
So the greatest common factor 39000 and 39014 is 2.

Also check out the Least Common Multiple of 39000 and 39014