What is the Greatest Common Factor of 27968 and 27987?

Greatest common factor (GCF) of 27968 and 27987 is 19.

GCF(27968,27987) = 19

We will now calculate the prime factors of 27968 and 27987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27968 and 27987.

How to find the GCF of 27968 and 27987?

We will first find the prime factorization of 27968 and 27987. After we will calculate the factors of 27968 and 27987 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 27987

Prime factors of 27987 are 3, 19, 491. Prime factorization of 27987 in exponential form is:

27987 = 3¹ × 19¹ × 491¹

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 27987

List of positive integer factors of 27987 that divides 27968 without a remainder.

1, 3, 19, 57, 491, 1473, 9329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27968 and 27987. The biggest common factor number is the GCF number.
So the greatest common factor 27968 and 27987 is 19.

Also check out the Least Common Multiple of 27968 and 27987