What is the Greatest Common Factor of 5760 and 5772?

Greatest common factor (GCF) of 5760 and 5772 is 12.

GCF(5760,5772) = 12

We will now calculate the prime factors of 5760 and 5772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5760 and 5772.

How to find the GCF of 5760 and 5772?

We will first find the prime factorization of 5760 and 5772. After we will calculate the factors of 5760 and 5772 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 5772

Prime factors of 5772 are 2, 3, 13, 37. Prime factorization of 5772 in exponential form is:

5772 = 2² × 3¹ × 13¹ × 37¹

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 5772

List of positive integer factors of 5772 that divides 5760 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 37, 39, 52, 74, 78, 111, 148, 156, 222, 444, 481, 962, 1443, 1924, 2886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5760 and 5772. The biggest common factor number is the GCF number.
So the greatest common factor 5760 and 5772 is 12.

Also check out the Least Common Multiple of 5760 and 5772