What is the Greatest Common Factor of 27974 and 27980?

Greatest common factor (GCF) of 27974 and 27980 is 2.

GCF(27974,27980) = 2

We will now calculate the prime factors of 27974 and 27980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27974 and 27980.

How to find the GCF of 27974 and 27980?

We will first find the prime factorization of 27974 and 27980. After we will calculate the factors of 27974 and 27980 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27980

Prime factors of 27980 are 2, 5, 1399. Prime factorization of 27980 in exponential form is:

27980 = 2² × 5¹ × 1399¹

Step-3: Factors of 27974

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

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

Step-4: Factors of 27980

List of positive integer factors of 27980 that divides 27974 without a remainder.

1, 2, 4, 5, 10, 20, 1399, 2798, 5596, 6995, 13990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27974 and 27980. The biggest common factor number is the GCF number.
So the greatest common factor 27974 and 27980 is 2.

Also check out the Least Common Multiple of 27974 and 27980