What is the Greatest Common Factor of 17984 and 17990?

Greatest common factor (GCF) of 17984 and 17990 is 2.

GCF(17984,17990) = 2

We will now calculate the prime factors of 17984 and 17990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17984 and 17990.

How to find the GCF of 17984 and 17990?

We will first find the prime factorization of 17984 and 17990. After we will calculate the factors of 17984 and 17990 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 17990

Prime factors of 17990 are 2, 5, 7, 257. Prime factorization of 17990 in exponential form is:

17990 = 2¹ × 5¹ × 7¹ × 257¹

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 17990

List of positive integer factors of 17990 that divides 17984 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 257, 514, 1285, 1799, 2570, 3598, 8995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17984 and 17990. The biggest common factor number is the GCF number.
So the greatest common factor 17984 and 17990 is 2.

Also check out the Least Common Multiple of 17984 and 17990