What is the Greatest Common Factor of 7680 and 7700?

Greatest common factor (GCF) of 7680 and 7700 is 20.

GCF(7680,7700) = 20

We will now calculate the prime factors of 7680 and 7700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7680 and 7700.

How to find the GCF of 7680 and 7700?

We will first find the prime factorization of 7680 and 7700. After we will calculate the factors of 7680 and 7700 and find the biggest common factor number .

Step-1: Prime Factorization of 7680

Prime factors of 7680 are 2, 3, 5. Prime factorization of 7680 in exponential form is:

7680 = 2⁹ × 3¹ × 5¹

Step-2: Prime Factorization of 7700

Prime factors of 7700 are 2, 5, 7, 11. Prime factorization of 7700 in exponential form is:

7700 = 2² × 5² × 7¹ × 11¹

Step-3: Factors of 7680

List of positive integer factors of 7680 that divides 7680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840

Step-4: Factors of 7700

List of positive integer factors of 7700 that divides 7680 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 50, 55, 70, 77, 100, 110, 140, 154, 175, 220, 275, 308, 350, 385, 550, 700, 770, 1100, 1540, 1925, 3850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7680 and 7700. The biggest common factor number is the GCF number.
So the greatest common factor 7680 and 7700 is 20.

Also check out the Least Common Multiple of 7680 and 7700