What is the Greatest Common Factor of 17005 and 17024?

Greatest common factor (GCF) of 17005 and 17024 is 19.

GCF(17005,17024) = 19

We will now calculate the prime factors of 17005 and 17024, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17005 and 17024.

How to find the GCF of 17005 and 17024?

We will first find the prime factorization of 17005 and 17024. After we will calculate the factors of 17005 and 17024 and find the biggest common factor number .

Step-1: Prime Factorization of 17005

Prime factors of 17005 are 5, 19, 179. Prime factorization of 17005 in exponential form is:

17005 = 5¹ × 19¹ × 179¹

Step-2: Prime Factorization of 17024

Prime factors of 17024 are 2, 7, 19. Prime factorization of 17024 in exponential form is:

17024 = 2⁷ × 7¹ × 19¹

Step-3: Factors of 17005

List of positive integer factors of 17005 that divides 17005 without a remainder.

1, 5, 19, 95, 179, 895, 3401

Step-4: Factors of 17024

List of positive integer factors of 17024 that divides 17005 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 128, 133, 152, 224, 266, 304, 448, 532, 608, 896, 1064, 1216, 2128, 2432, 4256, 8512

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17005 and 17024. The biggest common factor number is the GCF number.
So the greatest common factor 17005 and 17024 is 19.

Also check out the Least Common Multiple of 17005 and 17024