What is the Greatest Common Factor of 75984 and 75990?

Greatest common factor (GCF) of 75984 and 75990 is 6.

GCF(75984,75990) = 6

We will now calculate the prime factors of 75984 and 75990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75984 and 75990.

How to find the GCF of 75984 and 75990?

We will first find the prime factorization of 75984 and 75990. After we will calculate the factors of 75984 and 75990 and find the biggest common factor number .

Step-1: Prime Factorization of 75984

Prime factors of 75984 are 2, 3, 1583. Prime factorization of 75984 in exponential form is:

75984 = 2⁴ × 3¹ × 1583¹

Step-2: 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-3: Factors of 75984

List of positive integer factors of 75984 that divides 75984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1583, 3166, 4749, 6332, 9498, 12664, 18996, 25328, 37992

Step-4: Factors of 75990

List of positive integer factors of 75990 that divides 75984 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75984 and 75990. The biggest common factor number is the GCF number.
So the greatest common factor 75984 and 75990 is 6.

Also check out the Least Common Multiple of 75984 and 75990