What is the Greatest Common Factor of 14000 and 14014?

Greatest common factor (GCF) of 14000 and 14014 is 14.

GCF(14000,14014) = 14

We will now calculate the prime factors of 14000 and 14014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14000 and 14014.

How to find the GCF of 14000 and 14014?

We will first find the prime factorization of 14000 and 14014. After we will calculate the factors of 14000 and 14014 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 14014

Prime factors of 14014 are 2, 7, 11, 13. Prime factorization of 14014 in exponential form is:

14014 = 2¹ × 7² × 11¹ × 13¹

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 14014

List of positive integer factors of 14014 that divides 14000 without a remainder.

1, 2, 7, 11, 13, 14, 22, 26, 49, 77, 91, 98, 143, 154, 182, 286, 539, 637, 1001, 1078, 1274, 2002, 7007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14000 and 14014. The biggest common factor number is the GCF number.
So the greatest common factor 14000 and 14014 is 14.

Also check out the Least Common Multiple of 14000 and 14014