What is the Greatest Common Factor of 7582 and 7600?

Greatest common factor (GCF) of 7582 and 7600 is 2.

GCF(7582,7600) = 2

We will now calculate the prime factors of 7582 and 7600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7582 and 7600.

How to find the GCF of 7582 and 7600?

We will first find the prime factorization of 7582 and 7600. After we will calculate the factors of 7582 and 7600 and find the biggest common factor number .

Step-1: Prime Factorization of 7582

Prime factors of 7582 are 2, 17, 223. Prime factorization of 7582 in exponential form is:

7582 = 2¹ × 17¹ × 223¹

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 7582

List of positive integer factors of 7582 that divides 7582 without a remainder.

1, 2, 17, 34, 223, 446, 3791

Step-4: Factors of 7600

List of positive integer factors of 7600 that divides 7582 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 7582 and 7600. The biggest common factor number is the GCF number.
So the greatest common factor 7582 and 7600 is 2.

Also check out the Least Common Multiple of 7582 and 7600