What is the Greatest Common Factor of 71982 and 72000?

Greatest common factor (GCF) of 71982 and 72000 is 18.

GCF(71982,72000) = 18

We will now calculate the prime factors of 71982 and 72000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71982 and 72000.

How to find the GCF of 71982 and 72000?

We will first find the prime factorization of 71982 and 72000. After we will calculate the factors of 71982 and 72000 and find the biggest common factor number .

Step-1: Prime Factorization of 71982

Prime factors of 71982 are 2, 3, 31, 43. Prime factorization of 71982 in exponential form is:

71982 = 2¹ × 3³ × 31¹ × 43¹

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 71982

List of positive integer factors of 71982 that divides 71982 without a remainder.

1, 2, 3, 6, 9, 18, 27, 31, 43, 54, 62, 86, 93, 129, 186, 258, 279, 387, 558, 774, 837, 1161, 1333, 1674, 2322, 2666, 3999, 7998, 11997, 23994, 35991

Step-4: Factors of 72000

List of positive integer factors of 72000 that divides 71982 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 71982 and 72000. The biggest common factor number is the GCF number.
So the greatest common factor 71982 and 72000 is 18.

Also check out the Least Common Multiple of 71982 and 72000