What is the Greatest Common Factor of 5795 and 5814?

Greatest common factor (GCF) of 5795 and 5814 is 19.

GCF(5795,5814) = 19

We will now calculate the prime factors of 5795 and 5814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5795 and 5814.

How to find the GCF of 5795 and 5814?

We will first find the prime factorization of 5795 and 5814. After we will calculate the factors of 5795 and 5814 and find the biggest common factor number .

Step-1: Prime Factorization of 5795

Prime factors of 5795 are 5, 19, 61. Prime factorization of 5795 in exponential form is:

5795 = 5¹ × 19¹ × 61¹

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 5795

List of positive integer factors of 5795 that divides 5795 without a remainder.

1, 5, 19, 61, 95, 305, 1159

Step-4: Factors of 5814

List of positive integer factors of 5814 that divides 5795 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 5795 and 5814. The biggest common factor number is the GCF number.
So the greatest common factor 5795 and 5814 is 19.

Also check out the Least Common Multiple of 5795 and 5814