What is the Greatest Common Factor of 75966 and 75975?

Greatest common factor (GCF) of 75966 and 75975 is 3.

GCF(75966,75975) = 3

We will now calculate the prime factors of 75966 and 75975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75966 and 75975.

How to find the GCF of 75966 and 75975?

We will first find the prime factorization of 75966 and 75975. After we will calculate the factors of 75966 and 75975 and find the biggest common factor number .

Step-1: Prime Factorization of 75966

Prime factors of 75966 are 2, 3, 11, 1151. Prime factorization of 75966 in exponential form is:

75966 = 2¹ × 3¹ × 11¹ × 1151¹

Step-2: Prime Factorization of 75975

Prime factors of 75975 are 3, 5, 1013. Prime factorization of 75975 in exponential form is:

75975 = 3¹ × 5² × 1013¹

Step-3: Factors of 75966

List of positive integer factors of 75966 that divides 75966 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 1151, 2302, 3453, 6906, 12661, 25322, 37983

Step-4: Factors of 75975

List of positive integer factors of 75975 that divides 75966 without a remainder.

1, 3, 5, 15, 25, 75, 1013, 3039, 5065, 15195, 25325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75966 and 75975. The biggest common factor number is the GCF number.
So the greatest common factor 75966 and 75975 is 3.

Also check out the Least Common Multiple of 75966 and 75975