What is the Greatest Common Factor of 72306 and 72324?

Greatest common factor (GCF) of 72306 and 72324 is 18.

GCF(72306,72324) = 18

We will now calculate the prime factors of 72306 and 72324, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72306 and 72324.

How to find the GCF of 72306 and 72324?

We will first find the prime factorization of 72306 and 72324. After we will calculate the factors of 72306 and 72324 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 72324

Prime factors of 72324 are 2, 3, 7, 41. Prime factorization of 72324 in exponential form is:

72324 = 2² × 3² × 7² × 41¹

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 72324

List of positive integer factors of 72324 that divides 72306 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 41, 42, 49, 63, 82, 84, 98, 123, 126, 147, 164, 196, 246, 252, 287, 294, 369, 441, 492, 574, 588, 738, 861, 882, 1148, 1476, 1722, 1764, 2009, 2583, 3444, 4018, 5166, 6027, 8036, 10332, 12054, 18081, 24108, 36162

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72306 and 72324. The biggest common factor number is the GCF number.
So the greatest common factor 72306 and 72324 is 18.

Also check out the Least Common Multiple of 72306 and 72324