What is the Greatest Common Factor of 76000 and 76019?

Greatest common factor (GCF) of 76000 and 76019 is 19.

GCF(76000,76019) = 19

We will now calculate the prime factors of 76000 and 76019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76000 and 76019.

How to find the GCF of 76000 and 76019?

We will first find the prime factorization of 76000 and 76019. After we will calculate the factors of 76000 and 76019 and find the biggest common factor number .

Step-1: Prime Factorization of 76000

Prime factors of 76000 are 2, 5, 19. Prime factorization of 76000 in exponential form is:

76000 = 2⁵ × 5³ × 19¹

Step-2: Prime Factorization of 76019

Prime factors of 76019 are 19, 4001. Prime factorization of 76019 in exponential form is:

76019 = 19¹ × 4001¹

Step-3: Factors of 76000

List of positive integer factors of 76000 that divides 76000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 125, 152, 160, 190, 200, 250, 304, 380, 400, 475, 500, 608, 760, 800, 950, 1000, 1520, 1900, 2000, 2375, 3040, 3800, 4000, 4750, 7600, 9500, 15200, 19000, 38000

Step-4: Factors of 76019

List of positive integer factors of 76019 that divides 76000 without a remainder.

1, 19, 4001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76000 and 76019. The biggest common factor number is the GCF number.
So the greatest common factor 76000 and 76019 is 19.

Also check out the Least Common Multiple of 76000 and 76019