What is the Greatest Common Factor of 13984 and 14002?

Greatest common factor (GCF) of 13984 and 14002 is 2.

GCF(13984,14002) = 2

We will now calculate the prime factors of 13984 and 14002, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13984 and 14002.

How to find the GCF of 13984 and 14002?

We will first find the prime factorization of 13984 and 14002. After we will calculate the factors of 13984 and 14002 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 14002

Prime factors of 14002 are 2, 7001. Prime factorization of 14002 in exponential form is:

14002 = 2¹ × 7001¹

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 14002

List of positive integer factors of 14002 that divides 13984 without a remainder.

1, 2, 7001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13984 and 14002. The biggest common factor number is the GCF number.
So the greatest common factor 13984 and 14002 is 2.

Also check out the Least Common Multiple of 13984 and 14002