What is the Greatest Common Factor of 72189 and 72200?

Greatest common factor (GCF) of 72189 and 72200 is 1.

GCF(72189,72200) = 1

We will now calculate the prime factors of 72189 and 72200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72189 and 72200.

How to find the GCF of 72189 and 72200?

We will first find the prime factorization of 72189 and 72200. After we will calculate the factors of 72189 and 72200 and find the biggest common factor number .

Step-1: Prime Factorization of 72189

Prime factors of 72189 are 3, 13, 617. Prime factorization of 72189 in exponential form is:

72189 = 3² × 13¹ × 617¹

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 72189

List of positive integer factors of 72189 that divides 72189 without a remainder.

1, 3, 9, 13, 39, 117, 617, 1851, 5553, 8021, 24063

Step-4: Factors of 72200

List of positive integer factors of 72200 that divides 72189 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 72189 and 72200. The biggest common factor number is the GCF number.
So the greatest common factor 72189 and 72200 is 1.

Also check out the Least Common Multiple of 72189 and 72200