What is the Greatest Common Factor of 5760 and 5775?

Greatest common factor (GCF) of 5760 and 5775 is 15.

GCF(5760,5775) = 15

We will now calculate the prime factors of 5760 and 5775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5760 and 5775.

How to find the GCF of 5760 and 5775?

We will first find the prime factorization of 5760 and 5775. After we will calculate the factors of 5760 and 5775 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 5775

Prime factors of 5775 are 3, 5, 7, 11. Prime factorization of 5775 in exponential form is:

5775 = 3¹ × 5² × 7¹ × 11¹

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 5775

List of positive integer factors of 5775 that divides 5760 without a remainder.

1, 3, 5, 7, 11, 15, 21, 25, 33, 35, 55, 75, 77, 105, 165, 175, 231, 275, 385, 525, 825, 1155, 1925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5760 and 5775. The biggest common factor number is the GCF number.
So the greatest common factor 5760 and 5775 is 15.

Also check out the Least Common Multiple of 5760 and 5775