What is the Greatest Common Factor of 27189 and 27200?

Greatest common factor (GCF) of 27189 and 27200 is 1.

GCF(27189,27200) = 1

We will now calculate the prime factors of 27189 and 27200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27189 and 27200.

How to find the GCF of 27189 and 27200?

We will first find the prime factorization of 27189 and 27200. After we will calculate the factors of 27189 and 27200 and find the biggest common factor number .

Step-1: Prime Factorization of 27189

Prime factors of 27189 are 3, 19, 53. Prime factorization of 27189 in exponential form is:

27189 = 3³ × 19¹ × 53¹

Step-2: Prime Factorization of 27200

Prime factors of 27200 are 2, 5, 17. Prime factorization of 27200 in exponential form is:

27200 = 2⁶ × 5² × 17¹

Step-3: Factors of 27189

List of positive integer factors of 27189 that divides 27189 without a remainder.

1, 3, 9, 19, 27, 53, 57, 159, 171, 477, 513, 1007, 1431, 3021, 9063

Step-4: Factors of 27200

List of positive integer factors of 27200 that divides 27189 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 680, 800, 850, 1088, 1360, 1600, 1700, 2720, 3400, 5440, 6800, 13600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27189 and 27200. The biggest common factor number is the GCF number.
So the greatest common factor 27189 and 27200 is 1.

Also check out the Least Common Multiple of 27189 and 27200