What is the Greatest Common Factor of 75180 and 75187?

Greatest common factor (GCF) of 75180 and 75187 is 7.

GCF(75180,75187) = 7

We will now calculate the prime factors of 75180 and 75187, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75180 and 75187.

How to find the GCF of 75180 and 75187?

We will first find the prime factorization of 75180 and 75187. After we will calculate the factors of 75180 and 75187 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 75187

Prime factors of 75187 are 7, 23, 467. Prime factorization of 75187 in exponential form is:

75187 = 7¹ × 23¹ × 467¹

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 75187

List of positive integer factors of 75187 that divides 75180 without a remainder.

1, 7, 23, 161, 467, 3269, 10741

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75180 and 75187. The biggest common factor number is the GCF number.
So the greatest common factor 75180 and 75187 is 7.

Also check out the Least Common Multiple of 75180 and 75187