What is the Greatest Common Factor of 75200 and 75209?

Greatest common factor (GCF) of 75200 and 75209 is 1.

GCF(75200,75209) = 1

We will now calculate the prime factors of 75200 and 75209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75209.

How to find the GCF of 75200 and 75209?

We will first find the prime factorization of 75200 and 75209. After we will calculate the factors of 75200 and 75209 and find the biggest common factor number .

Step-1: Prime Factorization of 75200

Prime factors of 75200 are 2, 5, 47. Prime factorization of 75200 in exponential form is:

75200 = 2⁶ × 5² × 47¹

Step-2: Prime Factorization of 75209

Prime factors of 75209 are 75209. Prime factorization of 75209 in exponential form is:

75209 = 75209¹

Step-3: Factors of 75200

List of positive integer factors of 75200 that divides 75200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 47, 50, 64, 80, 94, 100, 160, 188, 200, 235, 320, 376, 400, 470, 752, 800, 940, 1175, 1504, 1600, 1880, 2350, 3008, 3760, 4700, 7520, 9400, 15040, 18800, 37600

Step-4: Factors of 75209

List of positive integer factors of 75209 that divides 75200 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75209. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75209 is 1.

Also check out the Least Common Multiple of 75200 and 75209