What is the Greatest Common Factor of 75990 and 76005?

Greatest common factor (GCF) of 75990 and 76005 is 15.

GCF(75990,76005) = 15

We will now calculate the prime factors of 75990 and 76005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75990 and 76005.

How to find the GCF of 75990 and 76005?

We will first find the prime factorization of 75990 and 76005. After we will calculate the factors of 75990 and 76005 and find the biggest common factor number .

Step-1: Prime Factorization of 75990

Prime factors of 75990 are 2, 3, 5, 17, 149. Prime factorization of 75990 in exponential form is:

75990 = 2¹ × 3¹ × 5¹ × 17¹ × 149¹

Step-2: Prime Factorization of 76005

Prime factors of 76005 are 3, 5, 563. Prime factorization of 76005 in exponential form is:

76005 = 3³ × 5¹ × 563¹

Step-3: Factors of 75990

List of positive integer factors of 75990 that divides 75990 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 149, 170, 255, 298, 447, 510, 745, 894, 1490, 2235, 2533, 4470, 5066, 7599, 12665, 15198, 25330, 37995

Step-4: Factors of 76005

List of positive integer factors of 76005 that divides 75990 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 563, 1689, 2815, 5067, 8445, 15201, 25335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75990 and 76005. The biggest common factor number is the GCF number.
So the greatest common factor 75990 and 76005 is 15.

Also check out the Least Common Multiple of 75990 and 76005