What is the Greatest Common Factor of 72000 and 72016?

Greatest common factor (GCF) of 72000 and 72016 is 16.

GCF(72000,72016) = 16

We will now calculate the prime factors of 72000 and 72016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72000 and 72016.

How to find the GCF of 72000 and 72016?

We will first find the prime factorization of 72000 and 72016. After we will calculate the factors of 72000 and 72016 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 72016

Prime factors of 72016 are 2, 7, 643. Prime factorization of 72016 in exponential form is:

72016 = 2⁴ × 7¹ × 643¹

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 72016

List of positive integer factors of 72016 that divides 72000 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 643, 1286, 2572, 4501, 5144, 9002, 10288, 18004, 36008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72000 and 72016. The biggest common factor number is the GCF number.
So the greatest common factor 72000 and 72016 is 16.

Also check out the Least Common Multiple of 72000 and 72016