What is the Greatest Common Factor of 75173 and 75180?

Greatest common factor (GCF) of 75173 and 75180 is 7.

GCF(75173,75180) = 7

We will now calculate the prime factors of 75173 and 75180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75173 and 75180.

How to find the GCF of 75173 and 75180?

We will first find the prime factorization of 75173 and 75180. After we will calculate the factors of 75173 and 75180 and find the biggest common factor number .

Step-1: Prime Factorization of 75173

Prime factors of 75173 are 7, 10739. Prime factorization of 75173 in exponential form is:

75173 = 7¹ × 10739¹

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 75173

List of positive integer factors of 75173 that divides 75173 without a remainder.

1, 7, 10739

Step-4: Factors of 75180

List of positive integer factors of 75180 that divides 75173 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 75173 and 75180. The biggest common factor number is the GCF number.
So the greatest common factor 75173 and 75180 is 7.

Also check out the Least Common Multiple of 75173 and 75180