What is the Greatest Common Factor of 5800 and 5814?

Greatest common factor (GCF) of 5800 and 5814 is 2.

GCF(5800,5814) = 2

We will now calculate the prime factors of 5800 and 5814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5800 and 5814.

How to find the GCF of 5800 and 5814?

We will first find the prime factorization of 5800 and 5814. After we will calculate the factors of 5800 and 5814 and find the biggest common factor number .

Step-1: Prime Factorization of 5800

Prime factors of 5800 are 2, 5, 29. Prime factorization of 5800 in exponential form is:

5800 = 2³ × 5² × 29¹

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 5800

List of positive integer factors of 5800 that divides 5800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 29, 40, 50, 58, 100, 116, 145, 200, 232, 290, 580, 725, 1160, 1450, 2900

Step-4: Factors of 5814

List of positive integer factors of 5814 that divides 5800 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 5800 and 5814. The biggest common factor number is the GCF number.
So the greatest common factor 5800 and 5814 is 2.

Also check out the Least Common Multiple of 5800 and 5814