What is the Greatest Common Factor of 71997 and 72009?

Greatest common factor (GCF) of 71997 and 72009 is 3.

GCF(71997,72009) = 3

We will now calculate the prime factors of 71997 and 72009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71997 and 72009.

How to find the GCF of 71997 and 72009?

We will first find the prime factorization of 71997 and 72009. After we will calculate the factors of 71997 and 72009 and find the biggest common factor number .

Step-1: Prime Factorization of 71997

Prime factors of 71997 are 3, 103, 233. Prime factorization of 71997 in exponential form is:

71997 = 3¹ × 103¹ × 233¹

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 71997

List of positive integer factors of 71997 that divides 71997 without a remainder.

1, 3, 103, 233, 309, 699, 23999

Step-4: Factors of 72009

List of positive integer factors of 72009 that divides 71997 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 71997 and 72009. The biggest common factor number is the GCF number.
So the greatest common factor 71997 and 72009 is 3.

Also check out the Least Common Multiple of 71997 and 72009