What is the Greatest Common Factor of 7584 and 7600?

Greatest common factor (GCF) of 7584 and 7600 is 16.

GCF(7584,7600) = 16

We will now calculate the prime factors of 7584 and 7600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7584 and 7600.

How to find the GCF of 7584 and 7600?

We will first find the prime factorization of 7584 and 7600. After we will calculate the factors of 7584 and 7600 and find the biggest common factor number .

Step-1: Prime Factorization of 7584

Prime factors of 7584 are 2, 3, 79. Prime factorization of 7584 in exponential form is:

7584 = 2⁵ × 3¹ × 79¹

Step-2: Prime Factorization of 7600

Prime factors of 7600 are 2, 5, 19. Prime factorization of 7600 in exponential form is:

7600 = 2⁴ × 5² × 19¹

Step-3: Factors of 7584

List of positive integer factors of 7584 that divides 7584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792

Step-4: Factors of 7600

List of positive integer factors of 7600 that divides 7584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 38, 40, 50, 76, 80, 95, 100, 152, 190, 200, 304, 380, 400, 475, 760, 950, 1520, 1900, 3800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7584 and 7600. The biggest common factor number is the GCF number.
So the greatest common factor 7584 and 7600 is 16.

Also check out the Least Common Multiple of 7584 and 7600