What is the Greatest Common Factor of 5797 and 5814?

Greatest common factor (GCF) of 5797 and 5814 is 17.

GCF(5797,5814) = 17

We will now calculate the prime factors of 5797 and 5814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5797 and 5814.

How to find the GCF of 5797 and 5814?

We will first find the prime factorization of 5797 and 5814. After we will calculate the factors of 5797 and 5814 and find the biggest common factor number .

Step-1: Prime Factorization of 5797

Prime factors of 5797 are 11, 17, 31. Prime factorization of 5797 in exponential form is:

5797 = 11¹ × 17¹ × 31¹

Step-2: Prime Factorization of 5814

Prime factors of 5814 are 2, 3, 17, 19. Prime factorization of 5814 in exponential form is:

5814 = 2¹ × 3² × 17¹ × 19¹

Step-3: Factors of 5797

List of positive integer factors of 5797 that divides 5797 without a remainder.

1, 11, 17, 31, 187, 341, 527

Step-4: Factors of 5814

List of positive integer factors of 5814 that divides 5797 without a remainder.

1, 2, 3, 6, 9, 17, 18, 19, 34, 38, 51, 57, 102, 114, 153, 171, 306, 323, 342, 646, 969, 1938, 2907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5797 and 5814. The biggest common factor number is the GCF number.
So the greatest common factor 5797 and 5814 is 17.

Also check out the Least Common Multiple of 5797 and 5814