What is the Greatest Common Factor of 71988 and 72000?

Greatest common factor (GCF) of 71988 and 72000 is 12.

GCF(71988,72000) = 12

We will now calculate the prime factors of 71988 and 72000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71988 and 72000.

How to find the GCF of 71988 and 72000?

We will first find the prime factorization of 71988 and 72000. After we will calculate the factors of 71988 and 72000 and find the biggest common factor number .

Step-1: Prime Factorization of 71988

Prime factors of 71988 are 2, 3, 7, 857. Prime factorization of 71988 in exponential form is:

71988 = 2² × 3¹ × 7¹ × 857¹

Step-2: Prime Factorization of 72000

Prime factors of 72000 are 2, 3, 5. Prime factorization of 72000 in exponential form is:

72000 = 2⁶ × 3² × 5³

Step-3: Factors of 71988

List of positive integer factors of 71988 that divides 71988 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 857, 1714, 2571, 3428, 5142, 5999, 10284, 11998, 17997, 23996, 35994

Step-4: Factors of 72000

List of positive integer factors of 72000 that divides 71988 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71988 and 72000. The biggest common factor number is the GCF number.
So the greatest common factor 71988 and 72000 is 12.

Also check out the Least Common Multiple of 71988 and 72000