What is the Greatest Common Factor of 72180 and 72198?

Greatest common factor (GCF) of 72180 and 72198 is 18.

GCF(72180,72198) = 18

We will now calculate the prime factors of 72180 and 72198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72180 and 72198.

How to find the GCF of 72180 and 72198?

We will first find the prime factorization of 72180 and 72198. After we will calculate the factors of 72180 and 72198 and find the biggest common factor number .

Step-1: Prime Factorization of 72180

Prime factors of 72180 are 2, 3, 5, 401. Prime factorization of 72180 in exponential form is:

72180 = 2² × 3² × 5¹ × 401¹

Step-2: 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-3: Factors of 72180

List of positive integer factors of 72180 that divides 72180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 401, 802, 1203, 1604, 2005, 2406, 3609, 4010, 4812, 6015, 7218, 8020, 12030, 14436, 18045, 24060, 36090

Step-4: Factors of 72198

List of positive integer factors of 72198 that divides 72180 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72180 and 72198. The biggest common factor number is the GCF number.
So the greatest common factor 72180 and 72198 is 18.

Also check out the Least Common Multiple of 72180 and 72198