What is the Greatest Common Factor of 75180 and 75200?

Greatest common factor (GCF) of 75180 and 75200 is 20.

GCF(75180,75200) = 20

We will now calculate the prime factors of 75180 and 75200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75180 and 75200.

How to find the GCF of 75180 and 75200?

We will first find the prime factorization of 75180 and 75200. After we will calculate the factors of 75180 and 75200 and find the biggest common factor number .

Step-1: Prime Factorization of 75180

Prime factors of 75180 are 2, 3, 5, 7, 179. Prime factorization of 75180 in exponential form is:

75180 = 2² × 3¹ × 5¹ × 7¹ × 179¹

Step-2: 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-3: Factors of 75180

List of positive integer factors of 75180 that divides 75180 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 179, 210, 358, 420, 537, 716, 895, 1074, 1253, 1790, 2148, 2506, 2685, 3580, 3759, 5012, 5370, 6265, 7518, 10740, 12530, 15036, 18795, 25060, 37590

Step-4: Factors of 75200

List of positive integer factors of 75200 that divides 75180 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75180 and 75200. The biggest common factor number is the GCF number.
So the greatest common factor 75180 and 75200 is 20.

Also check out the Least Common Multiple of 75180 and 75200