What is the Greatest Common Factor of 72000 and 72008?

Greatest common factor (GCF) of 72000 and 72008 is 8.

GCF(72000,72008) = 8

We will now calculate the prime factors of 72000 and 72008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72000 and 72008.

How to find the GCF of 72000 and 72008?

We will first find the prime factorization of 72000 and 72008. After we will calculate the factors of 72000 and 72008 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 72008

Prime factors of 72008 are 2, 9001. Prime factorization of 72008 in exponential form is:

72008 = 2³ × 9001¹

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 72008

List of positive integer factors of 72008 that divides 72000 without a remainder.

1, 2, 4, 8, 9001, 18002, 36004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72000 and 72008. The biggest common factor number is the GCF number.
So the greatest common factor 72000 and 72008 is 8.

Also check out the Least Common Multiple of 72000 and 72008