What is the Greatest Common Factor of 27989 and 28002?

Greatest common factor (GCF) of 27989 and 28002 is 13.

GCF(27989,28002) = 13

We will now calculate the prime factors of 27989 and 28002, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27989 and 28002.

How to find the GCF of 27989 and 28002?

We will first find the prime factorization of 27989 and 28002. After we will calculate the factors of 27989 and 28002 and find the biggest common factor number .

Step-1: Prime Factorization of 27989

Prime factors of 27989 are 13, 2153. Prime factorization of 27989 in exponential form is:

27989 = 13¹ × 2153¹

Step-2: Prime Factorization of 28002

Prime factors of 28002 are 2, 3, 13, 359. Prime factorization of 28002 in exponential form is:

28002 = 2¹ × 3¹ × 13¹ × 359¹

Step-3: Factors of 27989

List of positive integer factors of 27989 that divides 27989 without a remainder.

1, 13, 2153

Step-4: Factors of 28002

List of positive integer factors of 28002 that divides 27989 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 359, 718, 1077, 2154, 4667, 9334, 14001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27989 and 28002. The biggest common factor number is the GCF number.
So the greatest common factor 27989 and 28002 is 13.

Also check out the Least Common Multiple of 27989 and 28002