What is the Greatest Common Factor of 14000 and 14007?

Greatest common factor (GCF) of 14000 and 14007 is 7.

GCF(14000,14007) = 7

We will now calculate the prime factors of 14000 and 14007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14000 and 14007.

How to find the GCF of 14000 and 14007?

We will first find the prime factorization of 14000 and 14007. After we will calculate the factors of 14000 and 14007 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 14007

Prime factors of 14007 are 3, 7, 23, 29. Prime factorization of 14007 in exponential form is:

14007 = 3¹ × 7¹ × 23¹ × 29¹

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 14007

List of positive integer factors of 14007 that divides 14000 without a remainder.

1, 3, 7, 21, 23, 29, 69, 87, 161, 203, 483, 609, 667, 2001, 4669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14000 and 14007. The biggest common factor number is the GCF number.
So the greatest common factor 14000 and 14007 is 7.

Also check out the Least Common Multiple of 14000 and 14007