What is the Greatest Common Factor of 75060 and 75075?

Greatest common factor (GCF) of 75060 and 75075 is 15.

GCF(75060,75075) = 15

We will now calculate the prime factors of 75060 and 75075, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75060 and 75075.

How to find the GCF of 75060 and 75075?

We will first find the prime factorization of 75060 and 75075. After we will calculate the factors of 75060 and 75075 and find the biggest common factor number .

Step-1: Prime Factorization of 75060

Prime factors of 75060 are 2, 3, 5, 139. Prime factorization of 75060 in exponential form is:

75060 = 2² × 3³ × 5¹ × 139¹

Step-2: Prime Factorization of 75075

Prime factors of 75075 are 3, 5, 7, 11, 13. Prime factorization of 75075 in exponential form is:

75075 = 3¹ × 5² × 7¹ × 11¹ × 13¹

Step-3: Factors of 75060

List of positive integer factors of 75060 that divides 75060 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 139, 180, 270, 278, 417, 540, 556, 695, 834, 1251, 1390, 1668, 2085, 2502, 2780, 3753, 4170, 5004, 6255, 7506, 8340, 12510, 15012, 18765, 25020, 37530

Step-4: Factors of 75075

List of positive integer factors of 75075 that divides 75060 without a remainder.

1, 3, 5, 7, 11, 13, 15, 21, 25, 33, 35, 39, 55, 65, 75, 77, 91, 105, 143, 165, 175, 195, 231, 273, 275, 325, 385, 429, 455, 525, 715, 825, 975, 1001, 1155, 1365, 1925, 2145, 2275, 3003, 3575, 5005, 5775, 6825, 10725, 15015, 25025

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75060 and 75075. The biggest common factor number is the GCF number.
So the greatest common factor 75060 and 75075 is 15.

Also check out the Least Common Multiple of 75060 and 75075