What is the Greatest Common Factor of 5740 and 5749?

Greatest common factor (GCF) of 5740 and 5749 is 1.

GCF(5740,5749) = 1

We will now calculate the prime factors of 5740 and 5749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5740 and 5749.

How to find the GCF of 5740 and 5749?

We will first find the prime factorization of 5740 and 5749. After we will calculate the factors of 5740 and 5749 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 5749

Prime factors of 5749 are 5749. Prime factorization of 5749 in exponential form is:

5749 = 5749¹

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 5749

List of positive integer factors of 5749 that divides 5740 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5740 and 5749. The biggest common factor number is the GCF number.
So the greatest common factor 5740 and 5749 is 1.

Also check out the Least Common Multiple of 5740 and 5749