What is the Greatest Common Factor of 2560 and 2574?

Greatest common factor (GCF) of 2560 and 2574 is 2.

GCF(2560,2574) = 2

We will now calculate the prime factors of 2560 and 2574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2560 and 2574.

How to find the GCF of 2560 and 2574?

We will first find the prime factorization of 2560 and 2574. After we will calculate the factors of 2560 and 2574 and find the biggest common factor number .

Step-1: Prime Factorization of 2560

Prime factors of 2560 are 2, 5. Prime factorization of 2560 in exponential form is:

2560 = 2⁹ × 5¹

Step-2: Prime Factorization of 2574

Prime factors of 2574 are 2, 3, 11, 13. Prime factorization of 2574 in exponential form is:

2574 = 2¹ × 3² × 11¹ × 13¹

Step-3: Factors of 2560

List of positive integer factors of 2560 that divides 2560 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1280

Step-4: Factors of 2574

List of positive integer factors of 2574 that divides 2560 without a remainder.

1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 198, 234, 286, 429, 858, 1287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2560 and 2574. The biggest common factor number is the GCF number.
So the greatest common factor 2560 and 2574 is 2.

Also check out the Least Common Multiple of 2560 and 2574