What is the Greatest Common Factor of 75180 and 75185?

Greatest common factor (GCF) of 75180 and 75185 is 5.

GCF(75180,75185) = 5

We will now calculate the prime factors of 75180 and 75185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75180 and 75185.

How to find the GCF of 75180 and 75185?

We will first find the prime factorization of 75180 and 75185. After we will calculate the factors of 75180 and 75185 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 75185

Prime factors of 75185 are 5, 11, 1367. Prime factorization of 75185 in exponential form is:

75185 = 5¹ × 11¹ × 1367¹

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 75185

List of positive integer factors of 75185 that divides 75180 without a remainder.

1, 5, 11, 55, 1367, 6835, 15037

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75180 and 75185. The biggest common factor number is the GCF number.
So the greatest common factor 75180 and 75185 is 5.

Also check out the Least Common Multiple of 75180 and 75185