What is the Greatest Common Factor of 5814 and 5834?

Greatest common factor (GCF) of 5814 and 5834 is 2.

GCF(5814,5834) = 2

We will now calculate the prime factors of 5814 and 5834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5814 and 5834.

How to find the GCF of 5814 and 5834?

We will first find the prime factorization of 5814 and 5834. After we will calculate the factors of 5814 and 5834 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5834

Prime factors of 5834 are 2, 2917. Prime factorization of 5834 in exponential form is:

5834 = 2¹ × 2917¹

Step-3: Factors of 5814

List of positive integer factors of 5814 that divides 5814 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

Step-4: Factors of 5834

List of positive integer factors of 5834 that divides 5814 without a remainder.

1, 2, 2917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5814 and 5834. The biggest common factor number is the GCF number.
So the greatest common factor 5814 and 5834 is 2.

Also check out the Least Common Multiple of 5814 and 5834