What is the Greatest Common Factor of 14000 and 14020?

Greatest common factor (GCF) of 14000 and 14020 is 20.

GCF(14000,14020) = 20

We will now calculate the prime factors of 14000 and 14020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14000 and 14020.

How to find the GCF of 14000 and 14020?

We will first find the prime factorization of 14000 and 14020. After we will calculate the factors of 14000 and 14020 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 14020

Prime factors of 14020 are 2, 5, 701. Prime factorization of 14020 in exponential form is:

14020 = 2² × 5¹ × 701¹

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 14020

List of positive integer factors of 14020 that divides 14000 without a remainder.

1, 2, 4, 5, 10, 20, 701, 1402, 2804, 3505, 7010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14000 and 14020. The biggest common factor number is the GCF number.
So the greatest common factor 14000 and 14020 is 20.

Also check out the Least Common Multiple of 14000 and 14020