What is the Greatest Common Factor of 75075 and 75090?

Greatest common factor (GCF) of 75075 and 75090 is 15.

GCF(75075,75090) = 15

We will now calculate the prime factors of 75075 and 75090, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75075 and 75090.

How to find the GCF of 75075 and 75090?

We will first find the prime factorization of 75075 and 75090. After we will calculate the factors of 75075 and 75090 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75090

Prime factors of 75090 are 2, 3, 5, 2503. Prime factorization of 75090 in exponential form is:

75090 = 2¹ × 3¹ × 5¹ × 2503¹

Step-3: Factors of 75075

List of positive integer factors of 75075 that divides 75075 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

Step-4: Factors of 75090

List of positive integer factors of 75090 that divides 75075 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 2503, 5006, 7509, 12515, 15018, 25030, 37545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75075 and 75090. The biggest common factor number is the GCF number.
So the greatest common factor 75075 and 75090 is 15.

Also check out the Least Common Multiple of 75075 and 75090