What is the Greatest Common Factor of 19000 and 19019?

Greatest common factor (GCF) of 19000 and 19019 is 19.

GCF(19000,19019) = 19

We will now calculate the prime factors of 19000 and 19019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19000 and 19019.

How to find the GCF of 19000 and 19019?

We will first find the prime factorization of 19000 and 19019. After we will calculate the factors of 19000 and 19019 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 19019

Prime factors of 19019 are 7, 11, 13, 19. Prime factorization of 19019 in exponential form is:

19019 = 7¹ × 11¹ × 13¹ × 19¹

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 19019

List of positive integer factors of 19019 that divides 19000 without a remainder.

1, 7, 11, 13, 19, 77, 91, 133, 143, 209, 247, 1001, 1463, 1729, 2717

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19000 and 19019. The biggest common factor number is the GCF number.
So the greatest common factor 19000 and 19019 is 19.

Also check out the Least Common Multiple of 19000 and 19019