What is the Greatest Common Factor of 7665 and 7680?

Greatest common factor (GCF) of 7665 and 7680 is 15.

GCF(7665,7680) = 15

We will now calculate the prime factors of 7665 and 7680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7665 and 7680.

How to find the GCF of 7665 and 7680?

We will first find the prime factorization of 7665 and 7680. After we will calculate the factors of 7665 and 7680 and find the biggest common factor number .

Step-1: Prime Factorization of 7665

Prime factors of 7665 are 3, 5, 7, 73. Prime factorization of 7665 in exponential form is:

7665 = 3¹ × 5¹ × 7¹ × 73¹

Step-2: 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-3: Factors of 7665

List of positive integer factors of 7665 that divides 7665 without a remainder.

1, 3, 5, 7, 15, 21, 35, 73, 105, 219, 365, 511, 1095, 1533, 2555

Step-4: Factors of 7680

List of positive integer factors of 7680 that divides 7665 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7665 and 7680. The biggest common factor number is the GCF number.
So the greatest common factor 7665 and 7680 is 15.

Also check out the Least Common Multiple of 7665 and 7680