What is the Greatest Common Factor of 5814 and 5824?

Greatest common factor (GCF) of 5814 and 5824 is 2.

GCF(5814,5824) = 2

We will now calculate the prime factors of 5814 and 5824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5814 and 5824.

How to find the GCF of 5814 and 5824?

We will first find the prime factorization of 5814 and 5824. After we will calculate the factors of 5814 and 5824 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 5824

Prime factors of 5824 are 2, 7, 13. Prime factorization of 5824 in exponential form is:

5824 = 2⁶ × 7¹ × 13¹

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 5824

List of positive integer factors of 5824 that divides 5814 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 182, 208, 224, 364, 416, 448, 728, 832, 1456, 2912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5814 and 5824. The biggest common factor number is the GCF number.
So the greatest common factor 5814 and 5824 is 2.

Also check out the Least Common Multiple of 5814 and 5824