What is the Greatest Common Factor of 72180 and 72200?

Greatest common factor (GCF) of 72180 and 72200 is 20.

GCF(72180,72200) = 20

We will now calculate the prime factors of 72180 and 72200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72180 and 72200.

How to find the GCF of 72180 and 72200?

We will first find the prime factorization of 72180 and 72200. After we will calculate the factors of 72180 and 72200 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 72200

Prime factors of 72200 are 2, 5, 19. Prime factorization of 72200 in exponential form is:

72200 = 2³ × 5² × 19²

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 72200

List of positive integer factors of 72200 that divides 72180 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 361, 380, 475, 722, 760, 950, 1444, 1805, 1900, 2888, 3610, 3800, 7220, 9025, 14440, 18050, 36100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72180 and 72200. The biggest common factor number is the GCF number.
So the greatest common factor 72180 and 72200 is 20.

Also check out the Least Common Multiple of 72180 and 72200