What is the Greatest Common Factor of 13984 and 13994?

Greatest common factor (GCF) of 13984 and 13994 is 2.

GCF(13984,13994) = 2

We will now calculate the prime factors of 13984 and 13994, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13984 and 13994.

How to find the GCF of 13984 and 13994?

We will first find the prime factorization of 13984 and 13994. After we will calculate the factors of 13984 and 13994 and find the biggest common factor number .

Step-1: Prime Factorization of 13984

Prime factors of 13984 are 2, 19, 23. Prime factorization of 13984 in exponential form is:

13984 = 2⁵ × 19¹ × 23¹

Step-2: Prime Factorization of 13994

Prime factors of 13994 are 2, 6997. Prime factorization of 13994 in exponential form is:

13994 = 2¹ × 6997¹

Step-3: Factors of 13984

List of positive integer factors of 13984 that divides 13984 without a remainder.

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

Step-4: Factors of 13994

List of positive integer factors of 13994 that divides 13984 without a remainder.

1, 2, 6997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13984 and 13994. The biggest common factor number is the GCF number.
So the greatest common factor 13984 and 13994 is 2.

Also check out the Least Common Multiple of 13984 and 13994