What is the Greatest Common Factor of 2569 and 2576?

Greatest common factor (GCF) of 2569 and 2576 is 7.

GCF(2569,2576) = 7

We will now calculate the prime factors of 2569 and 2576, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2569 and 2576.

How to find the GCF of 2569 and 2576?

We will first find the prime factorization of 2569 and 2576. After we will calculate the factors of 2569 and 2576 and find the biggest common factor number .

Step-1: Prime Factorization of 2569

Prime factors of 2569 are 7, 367. Prime factorization of 2569 in exponential form is:

2569 = 7¹ × 367¹

Step-2: Prime Factorization of 2576

Prime factors of 2576 are 2, 7, 23. Prime factorization of 2576 in exponential form is:

2576 = 2⁴ × 7¹ × 23¹

Step-3: Factors of 2569

List of positive integer factors of 2569 that divides 2569 without a remainder.

1, 7, 367

Step-4: Factors of 2576

List of positive integer factors of 2576 that divides 2569 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 46, 56, 92, 112, 161, 184, 322, 368, 644, 1288

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2569 and 2576. The biggest common factor number is the GCF number.
So the greatest common factor 2569 and 2576 is 7.

Also check out the Least Common Multiple of 2569 and 2576