What is the Greatest Common Factor of 19000 and 19014?

Greatest common factor (GCF) of 19000 and 19014 is 2.

GCF(19000,19014) = 2

We will now calculate the prime factors of 19000 and 19014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19000 and 19014.

How to find the GCF of 19000 and 19014?

We will first find the prime factorization of 19000 and 19014. After we will calculate the factors of 19000 and 19014 and find the biggest common factor number .

Step-1: Prime Factorization of 19000

Prime factors of 19000 are 2, 5, 19. Prime factorization of 19000 in exponential form is:

19000 = 2³ × 5³ × 19¹

Step-2: Prime Factorization of 19014

Prime factors of 19014 are 2, 3, 3169. Prime factorization of 19014 in exponential form is:

19014 = 2¹ × 3¹ × 3169¹

Step-3: Factors of 19000

List of positive integer factors of 19000 that divides 19000 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 125, 152, 190, 200, 250, 380, 475, 500, 760, 950, 1000, 1900, 2375, 3800, 4750, 9500

Step-4: Factors of 19014

List of positive integer factors of 19014 that divides 19000 without a remainder.

1, 2, 3, 6, 3169, 6338, 9507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19000 and 19014. The biggest common factor number is the GCF number.
So the greatest common factor 19000 and 19014 is 2.

Also check out the Least Common Multiple of 19000 and 19014