What is the Greatest Common Factor of 28000 and 28014?

Greatest common factor (GCF) of 28000 and 28014 is 14.

GCF(28000,28014) = 14

We will now calculate the prime factors of 28000 and 28014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28000 and 28014.

How to find the GCF of 28000 and 28014?

We will first find the prime factorization of 28000 and 28014. After we will calculate the factors of 28000 and 28014 and find the biggest common factor number .

Step-1: Prime Factorization of 28000

Prime factors of 28000 are 2, 5, 7. Prime factorization of 28000 in exponential form is:

28000 = 2⁵ × 5³ × 7¹

Step-2: Prime Factorization of 28014

Prime factors of 28014 are 2, 3, 7, 23, 29. Prime factorization of 28014 in exponential form is:

28014 = 2¹ × 3¹ × 7¹ × 23¹ × 29¹

Step-3: Factors of 28000

List of positive integer factors of 28000 that divides 28000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 160, 175, 200, 224, 250, 280, 350, 400, 500, 560, 700, 800, 875, 1000, 1120, 1400, 1750, 2000, 2800, 3500, 4000, 5600, 7000, 14000

Step-4: Factors of 28014

List of positive integer factors of 28014 that divides 28000 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 29, 42, 46, 58, 69, 87, 138, 161, 174, 203, 322, 406, 483, 609, 667, 966, 1218, 1334, 2001, 4002, 4669, 9338, 14007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28000 and 28014. The biggest common factor number is the GCF number.
So the greatest common factor 28000 and 28014 is 14.

Also check out the Least Common Multiple of 28000 and 28014