What is the Greatest Common Factor of 72000 and 72005?

Greatest common factor (GCF) of 72000 and 72005 is 5.

GCF(72000,72005) = 5

We will now calculate the prime factors of 72000 and 72005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72000 and 72005.

How to find the GCF of 72000 and 72005?

We will first find the prime factorization of 72000 and 72005. After we will calculate the factors of 72000 and 72005 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 72005

Prime factors of 72005 are 5, 14401. Prime factorization of 72005 in exponential form is:

72005 = 5¹ × 14401¹

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 72005

List of positive integer factors of 72005 that divides 72000 without a remainder.

1, 5, 14401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72000 and 72005. The biggest common factor number is the GCF number.
So the greatest common factor 72000 and 72005 is 5.

Also check out the Least Common Multiple of 72000 and 72005