What is the Greatest Common Factor of 72009 and 72024?

Greatest common factor (GCF) of 72009 and 72024 is 3.

GCF(72009,72024) = 3

We will now calculate the prime factors of 72009 and 72024, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72009 and 72024.

How to find the GCF of 72009 and 72024?

We will first find the prime factorization of 72009 and 72024. After we will calculate the factors of 72009 and 72024 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 72024

Prime factors of 72024 are 2, 3, 3001. Prime factorization of 72024 in exponential form is:

72024 = 2³ × 3¹ × 3001¹

Step-3: Factors of 72009

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

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

Step-4: Factors of 72024

List of positive integer factors of 72024 that divides 72009 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 3001, 6002, 9003, 12004, 18006, 24008, 36012

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72009 and 72024. The biggest common factor number is the GCF number.
So the greatest common factor 72009 and 72024 is 3.

Also check out the Least Common Multiple of 72009 and 72024