What is the Greatest Common Factor of 72198 and 72216?

Greatest common factor (GCF) of 72198 and 72216 is 18.

GCF(72198,72216) = 18

We will now calculate the prime factors of 72198 and 72216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72198 and 72216.

How to find the GCF of 72198 and 72216?

We will first find the prime factorization of 72198 and 72216. After we will calculate the factors of 72198 and 72216 and find the biggest common factor number .

Step-1: Prime Factorization of 72198

Prime factors of 72198 are 2, 3, 7, 191. Prime factorization of 72198 in exponential form is:

72198 = 2¹ × 3³ × 7¹ × 191¹

Step-2: Prime Factorization of 72216

Prime factors of 72216 are 2, 3, 17, 59. Prime factorization of 72216 in exponential form is:

72216 = 2³ × 3² × 17¹ × 59¹

Step-3: Factors of 72198

List of positive integer factors of 72198 that divides 72198 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 191, 378, 382, 573, 1146, 1337, 1719, 2674, 3438, 4011, 5157, 8022, 10314, 12033, 24066, 36099

Step-4: Factors of 72216

List of positive integer factors of 72216 that divides 72198 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 59, 68, 72, 102, 118, 136, 153, 177, 204, 236, 306, 354, 408, 472, 531, 612, 708, 1003, 1062, 1224, 1416, 2006, 2124, 3009, 4012, 4248, 6018, 8024, 9027, 12036, 18054, 24072, 36108

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72198 and 72216. The biggest common factor number is the GCF number.
So the greatest common factor 72198 and 72216 is 18.

Also check out the Least Common Multiple of 72198 and 72216