What is the Greatest Common Factor of 76000 and 76009?

Greatest common factor (GCF) of 76000 and 76009 is 1.

GCF(76000,76009) = 1

We will now calculate the prime factors of 76000 and 76009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76000 and 76009.

How to find the GCF of 76000 and 76009?

We will first find the prime factorization of 76000 and 76009. After we will calculate the factors of 76000 and 76009 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 76009

Prime factors of 76009 are 29, 2621. Prime factorization of 76009 in exponential form is:

76009 = 29¹ × 2621¹

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 76009

List of positive integer factors of 76009 that divides 76000 without a remainder.

1, 29, 2621

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76000 and 76009. The biggest common factor number is the GCF number.
So the greatest common factor 76000 and 76009 is 1.

Also check out the Least Common Multiple of 76000 and 76009