What is the Greatest Common Factor of 75166 and 75180?

Greatest common factor (GCF) of 75166 and 75180 is 14.

GCF(75166,75180) = 14

We will now calculate the prime factors of 75166 and 75180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75166 and 75180.

How to find the GCF of 75166 and 75180?

We will first find the prime factorization of 75166 and 75180. After we will calculate the factors of 75166 and 75180 and find the biggest common factor number .

Step-1: Prime Factorization of 75166

Prime factors of 75166 are 2, 7, 13, 59. Prime factorization of 75166 in exponential form is:

75166 = 2¹ × 7² × 13¹ × 59¹

Step-2: 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-3: Factors of 75166

List of positive integer factors of 75166 that divides 75166 without a remainder.

1, 2, 7, 13, 14, 26, 49, 59, 91, 98, 118, 182, 413, 637, 767, 826, 1274, 1534, 2891, 5369, 5782, 10738, 37583

Step-4: Factors of 75180

List of positive integer factors of 75180 that divides 75166 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75166 and 75180. The biggest common factor number is the GCF number.
So the greatest common factor 75166 and 75180 is 14.

Also check out the Least Common Multiple of 75166 and 75180