What is the Greatest Common Factor of 17978 and 17984?

Greatest common factor (GCF) of 17978 and 17984 is 2.

GCF(17978,17984) = 2

We will now calculate the prime factors of 17978 and 17984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17978 and 17984.

How to find the GCF of 17978 and 17984?

We will first find the prime factorization of 17978 and 17984. After we will calculate the factors of 17978 and 17984 and find the biggest common factor number .

Step-1: Prime Factorization of 17978

Prime factors of 17978 are 2, 89, 101. Prime factorization of 17978 in exponential form is:

17978 = 2¹ × 89¹ × 101¹

Step-2: Prime Factorization of 17984

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

17984 = 2⁶ × 281¹

Step-3: Factors of 17978

List of positive integer factors of 17978 that divides 17978 without a remainder.

1, 2, 89, 101, 178, 202, 8989

Step-4: Factors of 17984

List of positive integer factors of 17984 that divides 17978 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17978 and 17984. The biggest common factor number is the GCF number.
So the greatest common factor 17978 and 17984 is 2.

Also check out the Least Common Multiple of 17978 and 17984