What is the Greatest Common Factor of 13980 and 14000?

Greatest common factor (GCF) of 13980 and 14000 is 20.

GCF(13980,14000) = 20

We will now calculate the prime factors of 13980 and 14000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13980 and 14000.

How to find the GCF of 13980 and 14000?

We will first find the prime factorization of 13980 and 14000. After we will calculate the factors of 13980 and 14000 and find the biggest common factor number .

Step-1: Prime Factorization of 13980

Prime factors of 13980 are 2, 3, 5, 233. Prime factorization of 13980 in exponential form is:

13980 = 2² × 3¹ × 5¹ × 233¹

Step-2: 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-3: Factors of 13980

List of positive integer factors of 13980 that divides 13980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 233, 466, 699, 932, 1165, 1398, 2330, 2796, 3495, 4660, 6990

Step-4: Factors of 14000

List of positive integer factors of 14000 that divides 13980 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13980 and 14000. The biggest common factor number is the GCF number.
So the greatest common factor 13980 and 14000 is 20.

Also check out the Least Common Multiple of 13980 and 14000