What is the Greatest Common Factor of 5814 and 5828?

Greatest common factor (GCF) of 5814 and 5828 is 2.

GCF(5814,5828) = 2

We will now calculate the prime factors of 5814 and 5828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5814 and 5828.

How to find the GCF of 5814 and 5828?

We will first find the prime factorization of 5814 and 5828. After we will calculate the factors of 5814 and 5828 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 5828

Prime factors of 5828 are 2, 31, 47. Prime factorization of 5828 in exponential form is:

5828 = 2² × 31¹ × 47¹

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 5828

List of positive integer factors of 5828 that divides 5814 without a remainder.

1, 2, 4, 31, 47, 62, 94, 124, 188, 1457, 2914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5814 and 5828. The biggest common factor number is the GCF number.
So the greatest common factor 5814 and 5828 is 2.

Also check out the Least Common Multiple of 5814 and 5828