What is the Greatest Common Factor of 75990 and 76000?

Greatest common factor (GCF) of 75990 and 76000 is 10.

GCF(75990,76000) = 10

We will now calculate the prime factors of 75990 and 76000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75990 and 76000.

How to find the GCF of 75990 and 76000?

We will first find the prime factorization of 75990 and 76000. After we will calculate the factors of 75990 and 76000 and find the biggest common factor number .

Step-1: Prime Factorization of 75990

Prime factors of 75990 are 2, 3, 5, 17, 149. Prime factorization of 75990 in exponential form is:

75990 = 2¹ × 3¹ × 5¹ × 17¹ × 149¹

Step-2: 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-3: Factors of 75990

List of positive integer factors of 75990 that divides 75990 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 149, 170, 255, 298, 447, 510, 745, 894, 1490, 2235, 2533, 4470, 5066, 7599, 12665, 15198, 25330, 37995

Step-4: Factors of 76000

List of positive integer factors of 76000 that divides 75990 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75990 and 76000. The biggest common factor number is the GCF number.
So the greatest common factor 75990 and 76000 is 10.

Also check out the Least Common Multiple of 75990 and 76000