What is the Greatest Common Factor of 5740 and 5745?

Greatest common factor (GCF) of 5740 and 5745 is 5.

GCF(5740,5745) = 5

We will now calculate the prime factors of 5740 and 5745, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5740 and 5745.

How to find the GCF of 5740 and 5745?

We will first find the prime factorization of 5740 and 5745. After we will calculate the factors of 5740 and 5745 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 5745

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

5745 = 3¹ × 5¹ × 383¹

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 5745

List of positive integer factors of 5745 that divides 5740 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5740 and 5745. The biggest common factor number is the GCF number.
So the greatest common factor 5740 and 5745 is 5.

Also check out the Least Common Multiple of 5740 and 5745