What is the Greatest Common Factor of 13984 and 14004?

Greatest common factor (GCF) of 13984 and 14004 is 4.

GCF(13984,14004) = 4

We will now calculate the prime factors of 13984 and 14004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13984 and 14004.

How to find the GCF of 13984 and 14004?

We will first find the prime factorization of 13984 and 14004. After we will calculate the factors of 13984 and 14004 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 14004

Prime factors of 14004 are 2, 3, 389. Prime factorization of 14004 in exponential form is:

14004 = 2² × 3² × 389¹

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 14004

List of positive integer factors of 14004 that divides 13984 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 389, 778, 1167, 1556, 2334, 3501, 4668, 7002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13984 and 14004. The biggest common factor number is the GCF number.
So the greatest common factor 13984 and 14004 is 4.

Also check out the Least Common Multiple of 13984 and 14004