What is the Greatest Common Factor of 5729 and 5740?

Greatest common factor (GCF) of 5729 and 5740 is 1.

GCF(5729,5740) = 1

We will now calculate the prime factors of 5729 and 5740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5729 and 5740.

How to find the GCF of 5729 and 5740?

We will first find the prime factorization of 5729 and 5740. After we will calculate the factors of 5729 and 5740 and find the biggest common factor number .

Step-1: Prime Factorization of 5729

Prime factors of 5729 are 17, 337. Prime factorization of 5729 in exponential form is:

5729 = 17¹ × 337¹

Step-2: 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-3: Factors of 5729

List of positive integer factors of 5729 that divides 5729 without a remainder.

1, 17, 337

Step-4: Factors of 5740

List of positive integer factors of 5740 that divides 5729 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5729 and 5740. The biggest common factor number is the GCF number.
So the greatest common factor 5729 and 5740 is 1.

Also check out the Least Common Multiple of 5729 and 5740