What is the Greatest Common Factor of 27968 and 27982?

Greatest common factor (GCF) of 27968 and 27982 is 2.

GCF(27968,27982) = 2

We will now calculate the prime factors of 27968 and 27982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27968 and 27982.

How to find the GCF of 27968 and 27982?

We will first find the prime factorization of 27968 and 27982. After we will calculate the factors of 27968 and 27982 and find the biggest common factor number .

Step-1: Prime Factorization of 27968

Prime factors of 27968 are 2, 19, 23. Prime factorization of 27968 in exponential form is:

27968 = 2⁶ × 19¹ × 23¹

Step-2: Prime Factorization of 27982

Prime factors of 27982 are 2, 17, 823. Prime factorization of 27982 in exponential form is:

27982 = 2¹ × 17¹ × 823¹

Step-3: Factors of 27968

List of positive integer factors of 27968 that divides 27968 without a remainder.

1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 64, 76, 92, 152, 184, 304, 368, 437, 608, 736, 874, 1216, 1472, 1748, 3496, 6992, 13984

Step-4: Factors of 27982

List of positive integer factors of 27982 that divides 27968 without a remainder.

1, 2, 17, 34, 823, 1646, 13991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27968 and 27982. The biggest common factor number is the GCF number.
So the greatest common factor 27968 and 27982 is 2.

Also check out the Least Common Multiple of 27968 and 27982