What is the Greatest Common Factor of 27964 and 27974?

Greatest common factor (GCF) of 27964 and 27974 is 2.

GCF(27964,27974) = 2

We will now calculate the prime factors of 27964 and 27974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27964 and 27974.

How to find the GCF of 27964 and 27974?

We will first find the prime factorization of 27964 and 27974. After we will calculate the factors of 27964 and 27974 and find the biggest common factor number .

Step-1: Prime Factorization of 27964

Prime factors of 27964 are 2, 6991. Prime factorization of 27964 in exponential form is:

27964 = 2² × 6991¹

Step-2: Prime Factorization of 27974

Prime factors of 27974 are 2, 71, 197. Prime factorization of 27974 in exponential form is:

27974 = 2¹ × 71¹ × 197¹

Step-3: Factors of 27964

List of positive integer factors of 27964 that divides 27964 without a remainder.

1, 2, 4, 6991, 13982

Step-4: Factors of 27974

List of positive integer factors of 27974 that divides 27964 without a remainder.

1, 2, 71, 142, 197, 394, 13987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27964 and 27974. The biggest common factor number is the GCF number.
So the greatest common factor 27964 and 27974 is 2.

Also check out the Least Common Multiple of 27964 and 27974