What is the Greatest Common Factor of 14994 and 15000?

Greatest common factor (GCF) of 14994 and 15000 is 6.

GCF(14994,15000) = 6

We will now calculate the prime factors of 14994 and 15000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14994 and 15000.

How to find the GCF of 14994 and 15000?

We will first find the prime factorization of 14994 and 15000. After we will calculate the factors of 14994 and 15000 and find the biggest common factor number .

Step-1: Prime Factorization of 14994

Prime factors of 14994 are 2, 3, 7, 17. Prime factorization of 14994 in exponential form is:

14994 = 2¹ × 3² × 7² × 17¹

Step-2: Prime Factorization of 15000

Prime factors of 15000 are 2, 3, 5. Prime factorization of 15000 in exponential form is:

15000 = 2³ × 3¹ × 5⁴

Step-3: Factors of 14994

List of positive integer factors of 14994 that divides 14994 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 49, 51, 63, 98, 102, 119, 126, 147, 153, 238, 294, 306, 357, 441, 714, 833, 882, 1071, 1666, 2142, 2499, 4998, 7497

Step-4: Factors of 15000

List of positive integer factors of 15000 that divides 14994 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 625, 750, 1000, 1250, 1500, 1875, 2500, 3000, 3750, 5000, 7500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14994 and 15000. The biggest common factor number is the GCF number.
So the greatest common factor 14994 and 15000 is 6.

Also check out the Least Common Multiple of 14994 and 15000