What is the Greatest Common Factor of 76989 and 77000?

Greatest common factor (GCF) of 76989 and 77000 is 11.

GCF(76989,77000) = 11

We will now calculate the prime factors of 76989 and 77000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76989 and 77000.

How to find the GCF of 76989 and 77000?

We will first find the prime factorization of 76989 and 77000. After we will calculate the factors of 76989 and 77000 and find the biggest common factor number .

Step-1: Prime Factorization of 76989

Prime factors of 76989 are 3, 11, 2333. Prime factorization of 76989 in exponential form is:

76989 = 3¹ × 11¹ × 2333¹

Step-2: Prime Factorization of 77000

Prime factors of 77000 are 2, 5, 7, 11. Prime factorization of 77000 in exponential form is:

77000 = 2³ × 5³ × 7¹ × 11¹

Step-3: Factors of 76989

List of positive integer factors of 76989 that divides 76989 without a remainder.

1, 3, 11, 33, 2333, 6999, 25663

Step-4: Factors of 77000

List of positive integer factors of 77000 that divides 76989 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 88, 100, 110, 125, 140, 154, 175, 200, 220, 250, 275, 280, 308, 350, 385, 440, 500, 550, 616, 700, 770, 875, 1000, 1100, 1375, 1400, 1540, 1750, 1925, 2200, 2750, 3080, 3500, 3850, 5500, 7000, 7700, 9625, 11000, 15400, 19250, 38500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76989 and 77000. The biggest common factor number is the GCF number.
So the greatest common factor 76989 and 77000 is 11.

Also check out the Least Common Multiple of 76989 and 77000