What is the Greatest Common Factor of 75200 and 75204?

Greatest common factor (GCF) of 75200 and 75204 is 4.

GCF(75200,75204) = 4

We will now calculate the prime factors of 75200 and 75204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75204.

How to find the GCF of 75200 and 75204?

We will first find the prime factorization of 75200 and 75204. After we will calculate the factors of 75200 and 75204 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 75204

Prime factors of 75204 are 2, 3, 2089. Prime factorization of 75204 in exponential form is:

75204 = 2² × 3² × 2089¹

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 75204

List of positive integer factors of 75204 that divides 75200 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2089, 4178, 6267, 8356, 12534, 18801, 25068, 37602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75204. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75204 is 4.

Also check out the Least Common Multiple of 75200 and 75204