What is the Greatest Common Factor of 72306 and 72319?

Greatest common factor (GCF) of 72306 and 72319 is 13.

GCF(72306,72319) = 13

We will now calculate the prime factors of 72306 and 72319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72306 and 72319.

How to find the GCF of 72306 and 72319?

We will first find the prime factorization of 72306 and 72319. After we will calculate the factors of 72306 and 72319 and find the biggest common factor number .

Step-1: Prime Factorization of 72306

Prime factors of 72306 are 2, 3, 13, 103. Prime factorization of 72306 in exponential form is:

72306 = 2¹ × 3³ × 13¹ × 103¹

Step-2: Prime Factorization of 72319

Prime factors of 72319 are 13, 5563. Prime factorization of 72319 in exponential form is:

72319 = 13¹ × 5563¹

Step-3: Factors of 72306

List of positive integer factors of 72306 that divides 72306 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 103, 117, 206, 234, 309, 351, 618, 702, 927, 1339, 1854, 2678, 2781, 4017, 5562, 8034, 12051, 24102, 36153

Step-4: Factors of 72319

List of positive integer factors of 72319 that divides 72306 without a remainder.

1, 13, 5563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72306 and 72319. The biggest common factor number is the GCF number.
So the greatest common factor 72306 and 72319 is 13.

Also check out the Least Common Multiple of 72306 and 72319