What is the Greatest Common Factor of 75180 and 75190?

Greatest common factor (GCF) of 75180 and 75190 is 10.

GCF(75180,75190) = 10

We will now calculate the prime factors of 75180 and 75190, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75180 and 75190.

How to find the GCF of 75180 and 75190?

We will first find the prime factorization of 75180 and 75190. After we will calculate the factors of 75180 and 75190 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 75190

Prime factors of 75190 are 2, 5, 73, 103. Prime factorization of 75190 in exponential form is:

75190 = 2¹ × 5¹ × 73¹ × 103¹

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 75190

List of positive integer factors of 75190 that divides 75180 without a remainder.

1, 2, 5, 10, 73, 103, 146, 206, 365, 515, 730, 1030, 7519, 15038, 37595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75180 and 75190. The biggest common factor number is the GCF number.
So the greatest common factor 75180 and 75190 is 10.

Also check out the Least Common Multiple of 75180 and 75190