What is the Greatest Common Factor of 27200 and 27209?

Greatest common factor (GCF) of 27200 and 27209 is 1.

GCF(27200,27209) = 1

We will now calculate the prime factors of 27200 and 27209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27200 and 27209.

How to find the GCF of 27200 and 27209?

We will first find the prime factorization of 27200 and 27209. After we will calculate the factors of 27200 and 27209 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27209

Prime factors of 27209 are 7, 13, 23. Prime factorization of 27209 in exponential form is:

27209 = 7¹ × 13² × 23¹

Step-3: Factors of 27200

List of positive integer factors of 27200 that divides 27200 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

Step-4: Factors of 27209

List of positive integer factors of 27209 that divides 27200 without a remainder.

1, 7, 13, 23, 91, 161, 169, 299, 1183, 2093, 3887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27200 and 27209. The biggest common factor number is the GCF number.
So the greatest common factor 27200 and 27209 is 1.

Also check out the Least Common Multiple of 27200 and 27209