What is the Greatest Common Factor of 59994 and 60000?

Greatest common factor (GCF) of 59994 and 60000 is 6.

GCF(59994,60000) = 6

We will now calculate the prime factors of 59994 and 60000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59994 and 60000.

How to find the GCF of 59994 and 60000?

We will first find the prime factorization of 59994 and 60000. After we will calculate the factors of 59994 and 60000 and find the biggest common factor number .

Step-1: Prime Factorization of 59994

Prime factors of 59994 are 2, 3, 11, 101. Prime factorization of 59994 in exponential form is:

59994 = 2¹ × 3³ × 11¹ × 101¹

Step-2: Prime Factorization of 60000

Prime factors of 60000 are 2, 3, 5. Prime factorization of 60000 in exponential form is:

60000 = 2⁵ × 3¹ × 5⁴

Step-3: Factors of 59994

List of positive integer factors of 59994 that divides 59994 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 101, 198, 202, 297, 303, 594, 606, 909, 1111, 1818, 2222, 2727, 3333, 5454, 6666, 9999, 19998, 29997

Step-4: Factors of 60000

List of positive integer factors of 60000 that divides 59994 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 625, 750, 800, 1000, 1200, 1250, 1500, 1875, 2000, 2400, 2500, 3000, 3750, 4000, 5000, 6000, 7500, 10000, 12000, 15000, 20000, 30000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59994 and 60000. The biggest common factor number is the GCF number.
So the greatest common factor 59994 and 60000 is 6.

Also check out the Least Common Multiple of 59994 and 60000