What is the Greatest Common Factor of 13984 and 13990?

Greatest common factor (GCF) of 13984 and 13990 is 2.

GCF(13984,13990) = 2

We will now calculate the prime factors of 13984 and 13990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13984 and 13990.

How to find the GCF of 13984 and 13990?

We will first find the prime factorization of 13984 and 13990. After we will calculate the factors of 13984 and 13990 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 13990

Prime factors of 13990 are 2, 5, 1399. Prime factorization of 13990 in exponential form is:

13990 = 2¹ × 5¹ × 1399¹

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 13990

List of positive integer factors of 13990 that divides 13984 without a remainder.

1, 2, 5, 10, 1399, 2798, 6995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13984 and 13990. The biggest common factor number is the GCF number.
So the greatest common factor 13984 and 13990 is 2.

Also check out the Least Common Multiple of 13984 and 13990