What is the Greatest Common Factor of 75200 and 75214?

Greatest common factor (GCF) of 75200 and 75214 is 2.

GCF(75200,75214) = 2

We will now calculate the prime factors of 75200 and 75214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75214.

How to find the GCF of 75200 and 75214?

We will first find the prime factorization of 75200 and 75214. After we will calculate the factors of 75200 and 75214 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 75214

Prime factors of 75214 are 2, 37607. Prime factorization of 75214 in exponential form is:

75214 = 2¹ × 37607¹

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 75214

List of positive integer factors of 75214 that divides 75200 without a remainder.

1, 2, 37607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75214. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75214 is 2.

Also check out the Least Common Multiple of 75200 and 75214