What is the Greatest Common Factor of 75200 and 75215?

Greatest common factor (GCF) of 75200 and 75215 is 5.

GCF(75200,75215) = 5

We will now calculate the prime factors of 75200 and 75215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75215.

How to find the GCF of 75200 and 75215?

We will first find the prime factorization of 75200 and 75215. After we will calculate the factors of 75200 and 75215 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 75215

Prime factors of 75215 are 5, 7, 307. Prime factorization of 75215 in exponential form is:

75215 = 5¹ × 7² × 307¹

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 75215

List of positive integer factors of 75215 that divides 75200 without a remainder.

1, 5, 7, 35, 49, 245, 307, 1535, 2149, 10745, 15043

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75215. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75215 is 5.

Also check out the Least Common Multiple of 75200 and 75215