What is the Greatest Common Factor of 75200 and 75220?

Greatest common factor (GCF) of 75200 and 75220 is 20.

GCF(75200,75220) = 20

We will now calculate the prime factors of 75200 and 75220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75220.

How to find the GCF of 75200 and 75220?

We will first find the prime factorization of 75200 and 75220. After we will calculate the factors of 75200 and 75220 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 75220

Prime factors of 75220 are 2, 5, 3761. Prime factorization of 75220 in exponential form is:

75220 = 2² × 5¹ × 3761¹

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 75220

List of positive integer factors of 75220 that divides 75200 without a remainder.

1, 2, 4, 5, 10, 20, 3761, 7522, 15044, 18805, 37610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75220. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75220 is 20.

Also check out the Least Common Multiple of 75200 and 75220