What is the Greatest Common Factor of 5760 and 5774?

Greatest common factor (GCF) of 5760 and 5774 is 2.

GCF(5760,5774) = 2

We will now calculate the prime factors of 5760 and 5774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5760 and 5774.

How to find the GCF of 5760 and 5774?

We will first find the prime factorization of 5760 and 5774. After we will calculate the factors of 5760 and 5774 and find the biggest common factor number .

Step-1: Prime Factorization of 5760

Prime factors of 5760 are 2, 3, 5. Prime factorization of 5760 in exponential form is:

5760 = 2⁷ × 3² × 5¹

Step-2: Prime Factorization of 5774

Prime factors of 5774 are 2, 2887. Prime factorization of 5774 in exponential form is:

5774 = 2¹ × 2887¹

Step-3: Factors of 5760

List of positive integer factors of 5760 that divides 5760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880

Step-4: Factors of 5774

List of positive integer factors of 5774 that divides 5760 without a remainder.

1, 2, 2887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5760 and 5774. The biggest common factor number is the GCF number.
So the greatest common factor 5760 and 5774 is 2.

Also check out the Least Common Multiple of 5760 and 5774