What is the Greatest Common Factor of 5740 and 5760?

Greatest common factor (GCF) of 5740 and 5760 is 20.

GCF(5740,5760) = 20

We will now calculate the prime factors of 5740 and 5760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5740 and 5760.

How to find the GCF of 5740 and 5760?

We will first find the prime factorization of 5740 and 5760. After we will calculate the factors of 5740 and 5760 and find the biggest common factor number .

Step-1: Prime Factorization of 5740

Prime factors of 5740 are 2, 5, 7, 41. Prime factorization of 5740 in exponential form is:

5740 = 2² × 5¹ × 7¹ × 41¹

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 5740

List of positive integer factors of 5740 that divides 5740 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 41, 70, 82, 140, 164, 205, 287, 410, 574, 820, 1148, 1435, 2870

Step-4: Factors of 5760

List of positive integer factors of 5760 that divides 5740 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 5740 and 5760. The biggest common factor number is the GCF number.
So the greatest common factor 5740 and 5760 is 20.

Also check out the Least Common Multiple of 5740 and 5760