What is the Greatest Common Factor of 7680 and 7696?

Greatest common factor (GCF) of 7680 and 7696 is 16.

GCF(7680,7696) = 16

We will now calculate the prime factors of 7680 and 7696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7680 and 7696.

How to find the GCF of 7680 and 7696?

We will first find the prime factorization of 7680 and 7696. After we will calculate the factors of 7680 and 7696 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 7696

Prime factors of 7696 are 2, 13, 37. Prime factorization of 7696 in exponential form is:

7696 = 2⁴ × 13¹ × 37¹

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 7696

List of positive integer factors of 7696 that divides 7680 without a remainder.

1, 2, 4, 8, 13, 16, 26, 37, 52, 74, 104, 148, 208, 296, 481, 592, 962, 1924, 3848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7680 and 7696. The biggest common factor number is the GCF number.
So the greatest common factor 7680 and 7696 is 16.

Also check out the Least Common Multiple of 7680 and 7696