What is the Greatest Common Factor of 75200 and 75216?

Greatest common factor (GCF) of 75200 and 75216 is 16.

GCF(75200,75216) = 16

We will now calculate the prime factors of 75200 and 75216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75200 and 75216.

How to find the GCF of 75200 and 75216?

We will first find the prime factorization of 75200 and 75216. After we will calculate the factors of 75200 and 75216 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 75216

Prime factors of 75216 are 2, 3, 1567. Prime factorization of 75216 in exponential form is:

75216 = 2⁴ × 3¹ × 1567¹

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 75216

List of positive integer factors of 75216 that divides 75200 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1567, 3134, 4701, 6268, 9402, 12536, 18804, 25072, 37608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75200 and 75216. The biggest common factor number is the GCF number.
So the greatest common factor 75200 and 75216 is 16.

Also check out the Least Common Multiple of 75200 and 75216