What is the Greatest Common Factor of 7564 and 7582?

Greatest common factor (GCF) of 7564 and 7582 is 2.

GCF(7564,7582) = 2

We will now calculate the prime factors of 7564 and 7582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7564 and 7582.

How to find the GCF of 7564 and 7582?

We will first find the prime factorization of 7564 and 7582. After we will calculate the factors of 7564 and 7582 and find the biggest common factor number .

Step-1: Prime Factorization of 7564

Prime factors of 7564 are 2, 31, 61. Prime factorization of 7564 in exponential form is:

7564 = 2² × 31¹ × 61¹

Step-2: 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-3: Factors of 7564

List of positive integer factors of 7564 that divides 7564 without a remainder.

1, 2, 4, 31, 61, 62, 122, 124, 244, 1891, 3782

Step-4: Factors of 7582

List of positive integer factors of 7582 that divides 7564 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7564 and 7582. The biggest common factor number is the GCF number.
So the greatest common factor 7564 and 7582 is 2.

Also check out the Least Common Multiple of 7564 and 7582