What is the Greatest Common Factor of 5978 and 5985?

Greatest common factor (GCF) of 5978 and 5985 is 7.

GCF(5978,5985) = 7

We will now calculate the prime factors of 5978 and 5985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5978 and 5985.

How to find the GCF of 5978 and 5985?

We will first find the prime factorization of 5978 and 5985. After we will calculate the factors of 5978 and 5985 and find the biggest common factor number .

Step-1: Prime Factorization of 5978

Prime factors of 5978 are 2, 7, 61. Prime factorization of 5978 in exponential form is:

5978 = 2¹ × 7² × 61¹

Step-2: Prime Factorization of 5985

Prime factors of 5985 are 3, 5, 7, 19. Prime factorization of 5985 in exponential form is:

5985 = 3² × 5¹ × 7¹ × 19¹

Step-3: Factors of 5978

List of positive integer factors of 5978 that divides 5978 without a remainder.

1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989

Step-4: Factors of 5985

List of positive integer factors of 5985 that divides 5978 without a remainder.

1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5978 and 5985. The biggest common factor number is the GCF number.
So the greatest common factor 5978 and 5985 is 7.

Also check out the Least Common Multiple of 5978 and 5985