What is the Greatest Common Factor of 17984 and 18004?

Greatest common factor (GCF) of 17984 and 18004 is 4.

GCF(17984,18004) = 4

We will now calculate the prime factors of 17984 and 18004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17984 and 18004.

How to find the GCF of 17984 and 18004?

We will first find the prime factorization of 17984 and 18004. After we will calculate the factors of 17984 and 18004 and find the biggest common factor number .

Step-1: Prime Factorization of 17984

Prime factors of 17984 are 2, 281. Prime factorization of 17984 in exponential form is:

17984 = 2⁶ × 281¹

Step-2: Prime Factorization of 18004

Prime factors of 18004 are 2, 7, 643. Prime factorization of 18004 in exponential form is:

18004 = 2² × 7¹ × 643¹

Step-3: Factors of 17984

List of positive integer factors of 17984 that divides 17984 without a remainder.

1, 2, 4, 8, 16, 32, 64, 281, 562, 1124, 2248, 4496, 8992

Step-4: Factors of 18004

List of positive integer factors of 18004 that divides 17984 without a remainder.

1, 2, 4, 7, 14, 28, 643, 1286, 2572, 4501, 9002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17984 and 18004. The biggest common factor number is the GCF number.
So the greatest common factor 17984 and 18004 is 4.

Also check out the Least Common Multiple of 17984 and 18004