What is the Greatest Common Factor of 14000 and 14017?

Greatest common factor (GCF) of 14000 and 14017 is 1.

GCF(14000,14017) = 1

We will now calculate the prime factors of 14000 and 14017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14000 and 14017.

How to find the GCF of 14000 and 14017?

We will first find the prime factorization of 14000 and 14017. After we will calculate the factors of 14000 and 14017 and find the biggest common factor number .

Step-1: Prime Factorization of 14000

Prime factors of 14000 are 2, 5, 7. Prime factorization of 14000 in exponential form is:

14000 = 2⁴ × 5³ × 7¹

Step-2: Prime Factorization of 14017

Prime factors of 14017 are 107, 131. Prime factorization of 14017 in exponential form is:

14017 = 107¹ × 131¹

Step-3: Factors of 14000

List of positive integer factors of 14000 that divides 14000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 175, 200, 250, 280, 350, 400, 500, 560, 700, 875, 1000, 1400, 1750, 2000, 2800, 3500, 7000

Step-4: Factors of 14017

List of positive integer factors of 14017 that divides 14000 without a remainder.

1, 107, 131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14000 and 14017. The biggest common factor number is the GCF number.
So the greatest common factor 14000 and 14017 is 1.

Also check out the Least Common Multiple of 14000 and 14017