What is the Greatest Common Factor of 72000 and 72009?

Greatest common factor (GCF) of 72000 and 72009 is 9.

GCF(72000,72009) = 9

We will now calculate the prime factors of 72000 and 72009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72000 and 72009.

How to find the GCF of 72000 and 72009?

We will first find the prime factorization of 72000 and 72009. After we will calculate the factors of 72000 and 72009 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 72009

Prime factors of 72009 are 3, 7, 127. Prime factorization of 72009 in exponential form is:

72009 = 3⁴ × 7¹ × 127¹

Step-3: Factors of 72000

List of positive integer factors of 72000 that divides 72000 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

Step-4: Factors of 72009

List of positive integer factors of 72009 that divides 72000 without a remainder.

1, 3, 7, 9, 21, 27, 63, 81, 127, 189, 381, 567, 889, 1143, 2667, 3429, 8001, 10287, 24003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72000 and 72009. The biggest common factor number is the GCF number.
So the greatest common factor 72000 and 72009 is 9.

Also check out the Least Common Multiple of 72000 and 72009