What is the Greatest Common Factor of 5760 and 5766?

Greatest common factor (GCF) of 5760 and 5766 is 6.

GCF(5760,5766) = 6

We will now calculate the prime factors of 5760 and 5766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5760 and 5766.

How to find the GCF of 5760 and 5766?

We will first find the prime factorization of 5760 and 5766. After we will calculate the factors of 5760 and 5766 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 5766

Prime factors of 5766 are 2, 3, 31. Prime factorization of 5766 in exponential form is:

5766 = 2¹ × 3¹ × 31²

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 5766

List of positive integer factors of 5766 that divides 5760 without a remainder.

1, 2, 3, 6, 31, 62, 93, 186, 961, 1922, 2883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5760 and 5766. The biggest common factor number is the GCF number.
So the greatest common factor 5760 and 5766 is 6.

Also check out the Least Common Multiple of 5760 and 5766