What is the Greatest Common Factor of 76000 and 76014?

Greatest common factor (GCF) of 76000 and 76014 is 2.

GCF(76000,76014) = 2

We will now calculate the prime factors of 76000 and 76014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76000 and 76014.

How to find the GCF of 76000 and 76014?

We will first find the prime factorization of 76000 and 76014. After we will calculate the factors of 76000 and 76014 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 76014

Prime factors of 76014 are 2, 3, 41, 103. Prime factorization of 76014 in exponential form is:

76014 = 2¹ × 3² × 41¹ × 103¹

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 76014

List of positive integer factors of 76014 that divides 76000 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 103, 123, 206, 246, 309, 369, 618, 738, 927, 1854, 4223, 8446, 12669, 25338, 38007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76000 and 76014. The biggest common factor number is the GCF number.
So the greatest common factor 76000 and 76014 is 2.

Also check out the Least Common Multiple of 76000 and 76014