What is the Greatest Common Factor of 72165 and 72180?

Greatest common factor (GCF) of 72165 and 72180 is 15.

GCF(72165,72180) = 15

We will now calculate the prime factors of 72165 and 72180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72165 and 72180.

How to find the GCF of 72165 and 72180?

We will first find the prime factorization of 72165 and 72180. After we will calculate the factors of 72165 and 72180 and find the biggest common factor number .

Step-1: Prime Factorization of 72165

Prime factors of 72165 are 3, 5, 17, 283. Prime factorization of 72165 in exponential form is:

72165 = 3¹ × 5¹ × 17¹ × 283¹

Step-2: 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-3: Factors of 72165

List of positive integer factors of 72165 that divides 72165 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 283, 849, 1415, 4245, 4811, 14433, 24055

Step-4: Factors of 72180

List of positive integer factors of 72180 that divides 72165 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72165 and 72180. The biggest common factor number is the GCF number.
So the greatest common factor 72165 and 72180 is 15.

Also check out the Least Common Multiple of 72165 and 72180