What is the Greatest Common Factor of 5745 and 5760?

Greatest common factor (GCF) of 5745 and 5760 is 15.

GCF(5745,5760) = 15

We will now calculate the prime factors of 5745 and 5760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5745 and 5760.

How to find the GCF of 5745 and 5760?

We will first find the prime factorization of 5745 and 5760. After we will calculate the factors of 5745 and 5760 and find the biggest common factor number .

Step-1: Prime Factorization of 5745

Prime factors of 5745 are 3, 5, 383. Prime factorization of 5745 in exponential form is:

5745 = 3¹ × 5¹ × 383¹

Step-2: 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-3: Factors of 5745

List of positive integer factors of 5745 that divides 5745 without a remainder.

1, 3, 5, 15, 383, 1149, 1915

Step-4: Factors of 5760

List of positive integer factors of 5760 that divides 5745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5745 and 5760. The biggest common factor number is the GCF number.
So the greatest common factor 5745 and 5760 is 15.

Also check out the Least Common Multiple of 5745 and 5760